Optimal investment and reinsurance policies for an insurer with ambiguity aversion

In this paper, we study the optimal investment and reinsurance problem for an insurer based on the variance premium principle, in which three cases are considered. First, we assume that the financial market does not exist. The insurer only holds an insurance business, and the optimal reinsurance problem is studied. Subsequently, we assume that there exists a financial market with an accurately modeled risky asset. The optimal investment and reinsurance problem is investigated under these conditions. Finally, we consider the general case in which the insurer is concerned about the model ambiguity of both the insurance market and the financial market. In all three cases, the value function is set to maximize the expected utility of terminal wealth. By employing the dynamic programming principle, we derive the Hamilton–Jacobi–Bellman (HJB) equations, which are satisfied by the value functions and obtain closed-form solutions for optimal reinsurance and investment policies and the value functions in all three cases. Most interestingly, we elucidate how investment improves the insurer’s utility and find that the existence of ambiguity can significantly affect the optimal policies and value functions. We also compare the ambiguities in the two markets and find that ambiguity in the insurance market has much more significant impact on the value function than the ambiguity in the financial market. It implies that it is more valuable for insurer to precisely evaluate the insurance risk. We also provide some numerical examples and economic explanations to illustrate our results.     

A model for irreversible investment with construction and revenue uncertainty

This paper presents a model of investment in projects that are characterized by uncertainty over both the construction costs and revenues. Both processes are modeled as spectrally negative Lévy jump-diffusions. The optimal stopping problem that determines the value of the project is solved under fairly general assumptions. It is found that the current value of the benefit-to-cost ratio (BCR) decreases in the frequency of negative shocks to the construction process. This implies that the cost overruns that can be expected if one ignores such shocks are increasing in their frequency. Based on calibrated data, the model is applied to the proposed construction of high-speed rail in the UK and it is found that its economic case cannot currently be made and is unlikely to be met at any time in the next decade. In addition it is found that ignoring construction uncertainty leads to a substantial probability of an erroneous decision being taken.     

Consumption paths under prospect utility in an optimal growth model

This paper studies the Cass-Koopmans-Ramsey model of optimal economic growth in the presence of loss aversion and habit formation. The representative agent's preferences for consumption can be gradually varied between the standard constant intertemporal elasticity of substitution (CIES) case and Kahneman and Tversky's prospect utility. We find that the transitional dynamics of optimal consumption paths differ distinctly from the standard model, in particular consumption smoothing is more pronounced. We also show that prospect utility can cause the economy to remain in a steady state with low consumption and low capital.     

Knightian uncertainty and insurance regulation decision

In contrast to insurance companies, regulatory authorities or regulators can obtain only limited information about the companies’ value. It hence leads to some effects on the regulation design, which is however often overlooked in the literature. This article characterizes the limited/imperfect information as Knightian (Risk, Uncertainty, and Profit, Houghton Mifflin, Boston, 1921) uncertainty (ambiguity). In order to stress the analytical effects of ambiguity on the regulation decisions, we firstly carry out an analysis in a standard immediate bankruptcy regulation where default and liquidation are considered as indistinguishable events. It is noticed that ambiguity-averse regulators require more “ambiguity equity”. We show then that under ambiguity an immediate liquidation policy delivers wrong liquidation with a positive probability. As an illustrative example to fix the wrong liquidation problem under ambiguity, a new regulation rule is developed with a regulatory auditing process. Based on this new model setup, we focus on examining how the riskiness of the firm’s value and the debt ratio affect liquidation probability.      

Subtle price discrimination and surplus extraction under uncertainty

This paper provides a solution to Proebsting’s Paradox, an argument that appears to show that the investment rule known as the Kelly criterion can lead a decision maker to invest a higher fraction of his wealth the more unfavorable the odds he faces are and, as a consequence, risk an arbitrarily high proportion of his wealth on the outcome of a single event. The paper shows that a large class of investment criteria, including ‘fractional Kelly’, also suffer from the same shortcoming and adapts ideas from the literature on price discrimination and surplus extraction to explain why this is so. The paper also presents a new criterion, dubbed the doubly conservative criterion, that is immune to the problem identified above. Immunity stems from the investor’s attitudes toward capital preservation and from him becoming rapidly pessimistic about his chances of winning the better odds he is offered.     

Risk, uncertainty, and option exercise

Many economic decisions can be described as an option exercise or optimal stopping problem under uncertainty. Motivated by experimental evidence such as the Ellsberg Paradox, we follow Knight (1921) and distinguish risk from uncertainty. To capture this distinction, we adopt the multiple-priors utility model. We show that the impact of ambiguity on the option exercise decision depends on the relative degrees of ambiguity about continuation payoffs and termination payoffs. Consequently, ambiguity may accelerate or delay option exercise. We apply our results to investment and exit problems, and show that the myopic NPV rule can be optimal for an agent having an extremely high degree of ambiguity aversion.     

Long-term wealth growth portfolio allocation under parameter uncertainty: A non-conservative robust approach

The Kelly portfolio, which is documented to have the highest wealth growth rate of any other portfolio in the long run, has highly risky and unstable performance in the short term. This paper offers a hybrid approach to address this problem by integrating the concept of ridge regression and shrinkage estimation into a robustly modified Kelly portfolio. The proposed approach is a two-stage optimization process that not only takes into account the effect of estimation error but also solves the notoriously conservative problem introduced by the robust optimization method. By extending the worst-case scenarios considered by the robust Kelly portfolio, our approach significantly improves its out-of-sample performance without compromising risk reduction. In an extensive out-of-sample analysis with simulated and empirical data sets, we also characterize the impacts of the robustness level and the length of the rolling window on the final result. Moreover, we conduct a comparative study to confirm the validity of the proposed approach, and our model allows the investor to have a better risk-return trade-off than other traditional models.     

Optimal Two‐part Pricing under Cost Uncertainty

This paper examines the optimal two‐part pricing under cost uncertainty. We consider a risk‐averse monopolistic firm that is subject to a cost shock to its constant marginal cost of production. The firm uses two‐part pricing to sell its output to a continuum of heterogeneous consumers. We show that the global and marginal effects of risk aversion on the firm's optimal two‐part pricing are to raise the unit price and lower the fixed payment. We further show that an increase in the fixed cost of production induces the firm to raise (lower) the unit price and lower (raise) the fixed payment under decreasing (increasing) absolute risk aversion. The firm's optimal two‐part pricing is unaffected by changes in the fixed cost under constant absolute risk aversion. Finally, we show that a mean‐preserving spread increase in cost uncertainty induces the firm to raise the unit price and lower the fixed payment under either decreasing or constant absolute risk aversion. Copyright © 2011 John Wiley & Sons, Ltd.     

Optimal monetary policy under incomplete markets and aggregate uncertainty: A long-run perspective

This paper examines the role of monetary policy in an environment with aggregate risk and incomplete markets. In a two-period overlapping-generations model with aggregate uncertainty, optimal monetary policy attains the ex-ante Pareto optimal allocation. This policy aims to stabilize the savings rate in the economy by changing real returns of nominal bonds via variation in expected inflation. Optimal expected inflation is procylical and on average higher than without uncertainty. Simple inflation targeting rules closely approximate the optimal monetary policy.     

Expected utility with uncertain probabilities theory

This paper introduces a model of decision making under ambiguity by extending the Bayesian approach to uncertain probabilities. In this model, preferences for ambiguity pertain directly to probabilities such that attitude toward ambiguity is defined as attitude toward mean-preserving spreads in probabilities—analogous to the Rothschild–Stiglitz risk attitude toward mean-preserving spreads in outcomes. The model refines the separations between tastes and beliefs, and between risk and ambiguity. These separations are crucial for the measurement of the degree of ambiguity and for the elicitation and characterization of attitudes toward ambiguity, thereby providing an empirically and experimentally applicable framework.     

Optimal capital accumulation under price uncertainty and costly reversibility

We consider the optimal capital accumulation policy of a competitive firm operating in the presence of decreasing returns to scale, price uncertainty, and costly reversibility of investment. We characterize the optimal accumulation policy and derive the value of the firm by focusing on the marginal investment decision and solving the associated optimal timing problem characterizing the option value of the associated opportunity to either disinvest or acquire a marginal unit of capacity. We also characterize the required exercise premia associated with the optimal policies and demonstrate that hysteresis prevails within this class of accumulation problems as well.     

Model uncertainty and intertemporal tax smoothing

In this paper we examine how model uncertainty due to the preference for robustness (RB) affects optimal taxation and the evolution of debt in the Barro tax-smoothing model (1979). We first study how the government spending shocks are absorbed in the short run by varying taxes or through debt under RB. Furthermore, we show that introducing RB improves the model׳s predictions by generating (i) the observed relative volatility of the changes in tax rates to government spending, (ii) the observed comovement between government deficits and spending, and (iii) more consistent behavior of government budget deficits in the U.S. economy. Finally, we show that RB can also improve the model׳s predictions in the presence of multiple shocks.     

Feasible sets,comparative risk aversion,and comparative uncertainty aversion in bargaining

We study feasible sets of the bargaining problem under two different assumptions: the players are subjective expected utility maximizers or the players are Choquet expected utility maximizers. For the latter case, we consider the effects on bargaining solutions when players become more risk averse and when they become more uncertainty averse.     

Integrating fundamental model uncertainty in policy analysis: A Bayesian averaging approach combining CGE-models with metamodeling techniques

Sustainable economic development in the future is driven by public policy on regional, national and global levels. Therefore a comprehensive policy analysis is needed that provides consistent and effective policy support. However, a general problem facing classical policy analysis is model uncertainty. All actors, those involved in the policy choice and those in the policy analysis, are fundamentally uncertain which of the different models corresponds to the true generative mechanism that represents the natural, economic, or social phenomena on which policy analysis is focused. In this paper, we propose a general framework that explicitly incorporates model uncertainty into the derivation of a policy choice. Incorporating model uncertainty into the analysis is limited by the very high required computational effort. In this regard, we apply metamodeling techniques as a way to reduce computational complexity. We demonstrate the effect of different metamodel types using a reduced model for the case of CAADP in Senegal. Furthermore, we explicitly show that ignoring model uncertainty leads to inefficient policy choices and results in a large waste of public resources.     

Optimal fiscal policy under learning

This paper characterizes optimal fiscal policy when agents learn about future taxation. A benevolent and fully rational government chooses taxes on labor income and state-contingent bonds to finance public spending, considering that private agents form their expectations through a learning algorithm. Facing a trade-off between distortionary taxes and distorted expectations, the Ramsey planner chooses the policy that minimizes the total cost of distortions. The analysis produces two main results. First, the government will use fiscal variables to manipulate expectations, reducing taxes and issuing debt at times of pessimism and doing the opposite at times of optimism. This speeds up learning. Second, the expectation-dependent fiscal plan is also history-dependent, and it prescribes taxes that are not as smooth and more persistent than under rational expectations. These findings are robust to alternative learning algorithms.     

Optimal investment with taxes: an existence result

We study the deterministic control problem of maximizing utility from consumption of an agent who seeks to optimally allocate his wealth between consumption and investment in a financial asset subject to taxes on benefits with first-in–first-out priority rule on sales. Short sales are prohibited and consumption is restricted to be non-negative. Such a problem has been introduced in a previous paper by the same authors where the first-order conditions have been derived. In this paper, we establish an existence result for this non-classical optimal control problem.