On the design of an optimal non-linear tax/pension system with habit formation

We study the optimal tax/pension design in a two-period model where individuals differ in both productivity and discount rates or projection bias and where their utility of the retirement period consumption is not independent of the earlier standard of living. We consider both welfarist and paternalistic social objectives. The paternalistic government attempts to correct the projection bias by using a higher discount factor. We derive general mathematical expressions that characterize optimal tax/pension design (marginal tax/subsidy rates). They suggest that the pattern of marginal labor income taxes depends on habit formation. Negative marginal labor income tax rates are possible. To gain a better understanding, we examine numerically the properties of an optimal lifetime redistribution policy with habit formation. We find support for non-linear tax/pension program in which some types of individuals are taxed while some are subsidized. The effect of changes in the degree of habit formation is explored in the numerical simulations as well as the implications of different degrees of correlation between skill and projection bias.     

Designing a linear pension scheme with forced savings and wage heterogeneity

This paper studies the optimal linear pension scheme when society consists of rational and myopic individuals. Myopic individuals have, ex ante, a strong preference for the present even though, ex post, they would regret not to have saved enough. While rational and myopic persons share the same ex post intertemporal preferences, only the rational agents make their savings and labor supply decisions according to these preferences. Individuals are also distinguished by their productivity. The social objective is “paternalistic”: the utilitarian welfare function depends on ex post utilities. We examine how the presence of myopic individuals affects both the size of the pension system and the degree of redistribution it operates, with and without liquidity constraints. The relationship between proportion of myopic individuals and characteristics of the pension system turns out to be much more complex than one would have conjectured. Neither the impact on the level of pensions nor the effect on their redistributive degree is unambiguous. Nevertheless, we show that under some plausible assumptions adding myopic individuals increases the level of pension benefits and leads to a shift from a flat or even targeted scheme to a partially contributory one. However, we also provide an example where the degree of redistribution is not a monotonic function of the proportion of myopic individuals.      

Strategic technology adoption and hedging under incomplete markets

We investigate the implications of technological innovation and non-diversifiable risk on entrepreneurial entry and optimal portfolio choice. In a real options model where two risk-averse individuals strategically decide on technology adoption, we show that the impact of non-diversifiable risk on the option timing decision is ambiguous and depends on the frequency of technological change. Compared to the complete market case, non-diversifiable risk may accelerate or delay the optimal investment decision. Moreover, strategic considerations regarding technology adoption play a central role for the entrepreneur’s optimal portfolio choice in the presence of non-diversifiable risk.     

A jackknife-type estimator for portfolio revision

This article proposes a novel approach to portfolio revision. The current literature on portfolio optimization uses a somewhat naïve approach, where portfolio weights are always completely revised after a predefined fixed period. However, one shortcoming of this procedure is that it ignores parameter uncertainty in the estimated portfolio weights, as well as the biasedness of the in-sample portfolio mean and variance as estimates of the expected portfolio return and out-of-sample variance. To rectify this problem, we propose a jackknife procedure to determine the optimal revision intensity, i.e. the percent of wealth that should be shifted to the new, in-sample optimal portfolio. We find that our approach leads to highly stable portfolio allocations over time, and can significantly reduce the turnover of several well established portfolio strategies. Moreover, the observed turnover reductions lead to statistically and economically significant performance gains in the presence of transaction costs.     

Optimal rules for ordering uncertain prospects

In this paper, we obtain the optimal selection rule for ordering uncertain prospects for all individuals with decreasing absolute risk averse utility functions. The optimal selection rule minimizes the admissible set of alternatives by discarding, from among a given set of alternatives, those that are inferior (for each utility function in the restricted class) to a member of the given set. We show that the Third Order Stochastic Dominance (TSD) rule is the optimal rule when comparing uncertain prospects with equal means. We also show that in the general case of unequal means, no known selection rule uses both necessary and sufficient conditions for dominance, and the TSD rule may be used to obtain a reasonable approximation to the smallest admissible set. The TSD rule is complex and we provide an efficient algorithm to obtain the TSD admissible set. For certain restrictive classes of the probability distributions (of returns on uncertain prospects) which cover most commonly used distributions in finance and economics, we obtain the optimal rule and show that it reduces to a simple form. We also study the relationship of the optimal selection rule to others previously advocated in the literature, including the more popular mean-variance rule as well as the semi-variance rule.     

Capital Structure and Debt Priority

We study a defaultable firm's debt priority structure in a simple structural model where the firm issues senior and junior bonds and is subject to both liquidity and solvency risks. Assuming that the absolute priority rule prevails and that liquidation is immediate upon default, we determine the firm's interior optimal priority structure along with its optimal capital structure. We also obtain closed‐form solutions for the market values of the firm's debt and equity. We find that the magnitude of the spread differential between junior and senior bond yields is positively, but not linearly related to the total debt level and the riskiness of assets. Finally, we provide an in‐depth analysis of probabilities of default and the term structure of credit spreads.     

IMITATION AND COORDINATION IN SMALL‐WORLD NETWORKS

We study aggregate behaviour in a setting where individuals repeatedly interact via a network to play a minimum‐effort (stag hunt) game. Of interest is whether play converges on the Pareto‐optimal or risk‐dominant outcome. We contrast the best‐reply dynamic with the imitate‐the‐best dynamic. We also contrast forms of lattice, small‐world and random networks. Our main finding is that play is far more likely to converge on the Pareto‐optimal outcome if individuals learn by imitation. We find that play in small‐world networks is similar to that in a regular network. Copyright © 2014 John Wiley & Sons, Ltd.     

Debt valuation, renegotiation, and optimal dividend policy

The valuation of debt and equity, reorganization boundaries,and firm's optimal dividend policies are studied in a frameworkwhere we model strategic interactions between debt holders andequity holders in a game-theoretic setting which can accommodatevarying bargaining powers to the two claimants. Two formulationsof reorganization are presented: debt-equity swaps and strategicdebt service resulting from negotiated debt service reductions.We study the effects of bond covenants on payout policies anddistinguish liquidity-induced defaults from strategic defaults.We derive optimal equity issuance and payout policies. The debtcapacity of the firm and the optimal capital structure are characterized.     

Optimal dividend policy and growth option

We analyse the interaction between the dividend policy and the decision on investment in a growth opportunity of a liquidity constrained firm. This leads us to study a mixed singular control/optimal stopping problem for a diffusion that we solve quasi-explicitly by establishing a connection with an optimal stopping problem. We characterize situations where it is optimal to postpone the distribution of dividends in order to invest at a subsequent date in the growth opportunity. We show that uncertainty and liquidity shocks have an ambiguous effect on the investment decision.      

Optimal Income Taxation and the Ability Distribution: Implications for Migration Equilibria

As recently argued by Diamond (1998), one of the key factors explaining the progressivity of an optimal non-linear income tax is the distribution of productivity among workers. Migration is one source of changes in the productivity distribution. How changes in the populations ability distribution affect optimal income tax schedules has received little attention. Changing the distribution generally affects both the objective function and the government budget constraint. We first consider the comparative statics of the fraction of highly-skilled workers with maximin and maximax welfare functions (so that only the second effect is present) and a quasi-linear utility function. We also present some results for a utilitarian social welfare function.We then study the interaction between mobility and redistributive taxation. We consider mobility by either the skilled or unskilled population under majority voting where governments take the population as fixed. If individuals choose to relocate independently, having identical ability distributions is always a stable equilibrium when the unskilled are the mobile group. However, this is not always the case when the skilled are mobile. If groups of individuals can choose where to locate, having identical ability distributions across regions is only an equilibrium when the mobile type has an overall majority.     

The Value of Interest Rate Stabilization Policies When Agents Are Learning

We examine the expectational stability (E-stability) of rational expectations equilibrium in the "New Keynesian" model where monetary policy is optimally derived and interest rate stabilization is added to the central bank's traditional objectives of inflation and output stabilization. We consider both the case where the central bank lacks a commitment technology and the case of full commitment. We show that for both cases, optimal policy rules yield rational expectations equilibria that are E-stable for a wide range of empirically plausible parameter values. These findings stand in contrast to Evans and Honkapohja's findings for optimal monetary policy rules in environments where interest rate stabilization is not a central bank objective.     

Near-sighted Justice

Chapter 11 structures complex negotiations between creditors and debtors that are overseen by a bankruptcy court. We identify conditions where the court should sometimes err in determining which firms should be liquidated. Such errors affect actions by both good and bad entrepreneurs. We first characterize the optimal error rate without renegotiation. When creditors and debtors can renegotiate to circumvent an error‐riven court, for one class of actions a blind court that ignores all information is optimal. For another class, the court should place the burden of proof on the entrepreneur. The robust feature is that the court should sometimes err.     

Mean-variance hedging for continuous processes: New proofs and examples

Let be a special semimartingale of the form and denote by the mean-variance tradeoff process of . Let be the space of predictable processes for which the stochastic integral is a square-integrable semimartingale. For a given constant and a given square-integrable random variable , the mean-variance optimal hedging strategy by definition minimizes the distance in between and the space . In financial terms, provides an approximation of the contingent claim by means of a self-financing trading strategy with minimal global risk. Assuming that is bounded and continuous, we first give a simple new proof of the closedness of in and of the existence of the F?llmer-Schweizer decomposition. If moreover is continuous and satisfies an additional condition, we can describe the mean-variance optimal strategy in feedback form, and we provide several examples where it can be computed explicitly. The additional condition states that the minimal and the variance-optimal martingale measures for should coincide. We provide examples where this assumption is satisfied, but we also show that it will typically fail if is not deterministic and includes exogenous randomness which is not induced by .     

Least-squares Importance Sampling for Monte Carlo security pricing

We describe a simple Importance Sampling strategy for Monte Carlo simulations based on a least-squares optimization procedure. With several numerical examples, we show that such Least-squares Importance Sampling (LSIS) provides efficiency gains comparable to the state-of-the-art techniques, for problems that can be formulated in terms of the determination of the optimal mean of a multivariate Gaussian distribution. In addition, LSIS can be naturally applied to more general Importance Sampling densities and is particularly effective when the ability to adjust higher moments of the sampling distribution, or to deal with non-Gaussian or multi-modal densities, is critical to achieve variance reductions.     

How investor demands for safety influence bank capital and liquidity trade-offs

We construct a model of a bank’s optimal funding choice, where the bank negotiates with both safety-driven short-term bondholders and (mostly) risk-taking long-term bondholders. We establish that investor demands for safety create a negative relationship between the bank’s capital choices and short-term funding, as well as negative relationships between capital and common measures of bank liquidity. Short-term investors’ demands for safety force the bank to hold more collateral, which diminishes the demands by long-term bondholders for higher holdings of bank capital. Consistent with our model, our bank-level empirical analysis of these capital–liquidity trade-offs shows that bank liquidity measures have a strong and negative relationship to the capital ratio. Furthermore, we show that this trade-off does not appear to be regulation related and has diminished in size over time.     

Risk Aversion,Downside Risk Aversion and Paying for Stochastic Improvements

This paper considers the relationship between risk preferences and the willingness to pay for stochastic improvements. We show that if the stochastic improvement satisfies a double-crossing condition, then a decision maker with utility v is willing to pay more than a decision maker with utility u, if v is both more risk averse and less downside risk averse than u. As the condition always holds in the case of self-protection, the result implies novel characterizations of individuals’ willingness to pay to reduce the probability of loss. By establishing a general result on the correspondence between an individual's willingness to pay, and his optimal purchase of stochastic improvement when there is a given relationship between stochastic improvements and the amount paid for them, we further show that all results on the willingness to pay can be applied directly to characterize the conditions under which a more risk averse individual will optimally choose to buy more stochastic improvement. Generalizations of existing results on optimal choice of self-protection can be obtained as corollaries.     

On the price of risk in a mean-risk optimization model

We investigate a mean-risk model for portfolio optimization where the risk quantifier is selected as a semi-deviation or as a standard deviation of the portfolio return. We analyse the existence of solutions to the problem under general assumptions. When the short positions are not constrained, we establish a lower bound on the cost of risk associated with optimizing the mean–standard deviation model and show that optimal solutions do not exist for any positive price of risk which is smaller than that bound. If the investment allocations are constrained, then we obtain a lower bound on the price of risk in terms of the shadow prices of said constraints and the data of the problem. A Value-at-Risk constraint in the model implies an upper bound on the price of risk for all feasible portfolios. Furthermore, we provide conditions under which using this upper bound as the cost of risk parameter in the model provides a non-dominated optimal portfolio with respect to the second-order stochastic dominance. Additionally, we study the relationship between minimizing the mean–standard deviation objective and maximizing the coefficient of variation and show that both problems are equivalent when the upper bound is used as the cost of risk. Additional relations between the Value-at-Risk constraint and the coefficient of variation are discussed as well. We illustrate the results numerically.     

Switching to a poor business activity: optimal capital structure, agency costs and covenant rules

We address the issue of modeling and quantifying the asset substitution problem in a setting where equityholders decisions alter both the volatility and the return of the firm cash flows. Our results contrast with those obtained in models where the agency problem is reduced to a pure risk-shifting problem. We find larger agency costs and lower optimal leverages. We identify the bankruptcy trigger written in debt indenture, which maximizes ex-ante firm value, given that equityholders will ex-post be able to risk-shift. Our model highlights the tradeoff between ex-post inefficient behavior of equityholders and inefficient covenant restrictions.      

Market or limit orders?

In this paper we investigate the problem of optimal order placement of an asset listed on an exchange using both market and limit orders in a simple model of market dynamics. We seek to understand under which settings it is optimal to place limit or market orders. Limit orders typically lower transaction costs but increase the risk of incomplete order execution, whereas market orders typically have higher transaction costs but are guaranteed to be executed. Rather than considering order book dynamics to determine if a limit order is executed we rely on price dynamics for this. We look at implementation shortfall in this setup with market impact of trading and propose a dynamic program to find the optimal placement of both market and limit orders for risk-neutral and risk-averse traders. With this we find a bound on the expected cost of trading and show that a trader who behaves optimally should always expect to pay less to trade less. We then solve the dynamic program numerically and examine optimal order placement strategies. We find that the decision between market and limit orders is sensitive to price volatility, risk aversion, and trading costs.     

Optimal Reinsurance Under the Risk-Adjusted Value of an Insurer’s Liability and an Economic Reinsurance Premium Principle

In this article, an optimal reinsurance problem is formulated from the perspective of an insurer, with the objective of minimizing the risk-adjusted value of its liability where the valuation is carried out by a cost-of-capital approach and the capital at risk is calculated by either the value-at-risk (VaR) or conditional value-at-risk (CVaR). In our reinsurance arrangement, we also assume that both insurer and reinsurer are obligated to pay more for a larger realization of loss as a way of reducing ex post moral hazard. A key contribution of this article is to expand the research on optimal reinsurance by deriving explicit optimal reinsurance solutions under an economic premium principle. It is a rather general class of premium principles that includes many weighted premium principles as special cases. The advantage of adopting such a premium principle is that the resulting reinsurance premium depends not only on the risk ceded but also on a market economic factor that reflects the market environment or the risk the reinsurer is facing. This feature appears to be more consistent with the reinsurance market. We show that the optimal reinsurance policies are piecewise linear under both VaR and CVaR risk measures. While the structures of optimal reinsurance solutions are the same for both risk measures, we also formally show that there are some significant differences, particularly on the managing tail risk. Because of the integration of the market factor (via the reinsurance pricing) into the optimal reinsurance model, some new insights on the optimal reinsurance design could be gleaned, which would otherwise be impossible for many of the existing models. For example, the market factor has a nontrivial effect on the optimal reinsurance, which is greatly influenced by the changes of the joint distribution of the market factor and the loss. Finally, under an additional assumption that the market factor and the loss have a copula with quadratic sections, we demonstrate that the optimal reinsurance policies admit relatively simple forms to foster the applicability of our theoretical results, and a numerical example is presented to further highlight our results.