Hedging under multiple risk constraints

Motivated by the asset–liability management problems under shortfall risk constraints, we consider in a general discrete-time framework the problem of finding the least expensive portfolio whose shortfalls with respect to a given set of stochastic benchmarks are bounded by a specific shortfall risk measure. We first show how the price of this portfolio may be computed recursively by dynamic programming for different shortfall risk measures, in complete and incomplete markets. We then focus on the specific situation where the shortfall risk constraints are imposed at each period on the next-period shortfalls, and obtain explicit results. Finally, we apply our results to a realistic asset–liability management problem of an energy company, and show how the shortfall risk constraints affect the optimal hedging of liabilities.     

Dynamic trading under integer constraints

In this paper, we investigate discrete-time trading under integer constraints, that is, we assume that the offered goods or shares are traded in integer quantities instead of the usual real quantity assumption. For finite probability spaces and rational asset prices, this has little effect on the core of the theory of no-arbitrage pricing. For price processes not restricted to the rational numbers, a novel theory of integer-arbitrage-free pricing and hedging emerges. We establish an FTAP, involving a set of absolutely continuous martingale measures satisfying an additional property. The set of prices of a contingent claim is not necessarily an interval, but is either empty or dense in an interval. We also discuss superhedging with integer-valued portfolios.     

Insurance premiums under demand constraints

Abstract

An alternative approach to the variance principle of premium determination is explored. The approach rationalises the principle in terms of an economic theory and formalises the notion that loadings in addition to the ‘fair’ premium are related to competition and expenses.     

Currency hedging for multinationals under liquidity constraints

This paper examines the impact of liquidity risk on the behavior of a risk-averse multinational firm (MNF) under exchange rate uncertainty in a two-period dynamic setting. The MNF has operations domiciled in the home country and in a foreign country, each of which produces a single homogeneous good to be sold in the home and foreign markets. To hedge the exchange rate risk, the MNF has access to one-period currency futures and option contracts in each period. The MNF is liquidity constrained in that it is obliged to terminate its risk management program in the second period whenever the net loss due to its first-period hedge position exceeds a predetermined threshold level. We show that the MNF optimally sells less (more) and produces more (less) in the foreign (home) country in response to the imposition of the liquidity constraint. We show further that the liquidity constrained MNF optimally uses the currency option contracts in the first period for hedging purposes in general, and opts for a long option position if its utility function is quadratic in particular.     

Optimal replication of contingent claims under portfolio constraints

We determine the minimum cost of super-replicating a nonnegativecontingent claim when there are convex constraints on portfolioweights. We show that the optimal cost with constraints is equalto the price of a related claim without constraints. The relatedclaim is a dominating claim, that is, a claim whose payoffsare increased in an appropriate way relative to the originalclaim. The results hold for a variety of options, includingsome path-dependent options. Constraints on the gamma of thereplicating portfolio, constraints on the portfolio amounts,and constraints on the number of shares are also considered.     

Performance measurement for investment decisions under capital constraints

An owner delegates investment decisions to a better informed manager whose time preferences are unknown to the owner. Due to exogenous capital constraints, not all profitable projects can be undertaken, and therefore the owner wants the manager to select the NPV-maximizing set of projects. We show that the relative benefit cost allocation scheme proposed by prior literature does not solve this problem. Adopting the same information structure as in Rogerson (J Polit Econ 105, 770–795, 1997) and Reichelstein (Rev Account Stud 2, 157–180, 1997), we demonstrate how to obtain robust goal congruence using residual income. The resulting revenue recognition and cost allocation rules lead to a performance measure reflecting the expected NPV-ranking of projects in each and every period.

How corporate governance affects payout policy under agency problems and external financing constraints

This paper analyzes the effect of corporate governance on the payout policy when a firm has both agency problems and external financing constraints. We empirically test whether strong corporate governance would lead to higher payout to minimize agency problems (outcome hypothesis), or to lower payout to avoid costly external financing (substitute hypothesis). We find that firms with higher (lower) external financing constraints tend to decrease (increase) payout ratio with an improvement in their corporate governance. The results are consistent with our hypothesis that the relation between payout and corporate governance is reversed depending on the relative sizes of agency and external financing costs.     

Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model

A drawdown constraint forces the current wealth to remain above a given function of its maximum to date. We consider the portfolio optimisation problem of maximising the long-term growth rate of the expected utility of wealth subject to a drawdown constraint, as in the original setup of Grossman and Zhou (Math. Finance 3:241–276, 1993). We work in an abstract semimartingale financial market model with a general class of utility functions and drawdown constraints. We solve the problem by showing that it is in fact equivalent to an unconstrained problem with a suitably modified utility function. Both the value function and the optimal investment policy for the drawdown problem are given explicitly in terms of their counterparts in the unconstrained problem.     

Upper bounds on stop-loss premiums under constraints on claim size distribution

Abstract

The problem of maximal stop-loss premium under prescribed constraints on claim size distribution is taken up again. The methods of linear programming are used to show that the recent results of others are intuitively obvious. These results are then extended by the linear programming technique to cases of more general constraints, e.g. prescribed claim size variance, or prescribed minimum frequency of excess claims. In particular it is shown that, typically, the upper bound on stop-loss premiums is generated by a claim size distribution which has all its mass concentrated at very few points. In contrast with the results obtained by others recently, it is seen that the claim size distribution which produces the maximal stop-loss premium is not generally independent of the excess. Some numerical examples are given showing that the methods used here can sometimes improve considerably the recent results of others. The case of a compound Poisson distribution is treated briefly.     

Political constraints, organization design and performance measurement in China’s state-owned enterprises

This study develops a theoretical model to test how political constraints on labor decisions mediate the effects of economic liberalization forces on aspects of organizational design such as delegation, performance measurement, and incentives in Chinese state-owned enterprises. Hypotheses tests using a large survey of divisional managers generally confirm the model: that the influence of three liberalization forces (industry level growth and foreign firm competition, joint venture experience and stock market listing) on organization design is mediated by political constraints.     

Optimal design of securities under asymmetric information

A firm must decide what security to sell to raise external capitalto finance a profitable investment opportunity. There is exante asymmetry of information regarding the probability distributionof cashflow generated by the investment. In this setting, wederive necessary and sufficient conditions for a security tobe optimal (uniquely optimal), that is, for pooling at thissecurity to be an (the unique) equilibrium outcome. Using theseconditions we show that the debt contract is (uniquely) optimalif and only if cash flows are ordered by (strict) conditionalstochastic dominance. Finally, we derive an equivalence relationshipbetween optimal security designs and designs that minimize mispricing.     

Optimal dividend policies for a class of growth-restricted diffusion processes under transaction costs and solvency constraints

In this paper, we consider a company whose surplus follows a rather general diffusion process and whose objective is to maximize expected discounted dividend payments. With each dividend payment, there are transaction costs and taxes, and it is shown in Paulsen (Adv. Appl. Probab. 39:669?C689, 2007) that under some reasonable assumptions, optimality is achieved by using a lump sum dividend barrier strategy, i.e., there is an upper barrier $\bar{u}^{*}$ and a lower barrier $\underline{u}^{*}$ so that whenever the surplus reaches $\bar{u}^{*}$ , it is reduced to $\underline{u}^{*}$ through a dividend payment. However, these optimal barriers may be unacceptably low from a solvency point of view. It is argued that, in that case, one should still look for a barrier strategy, but with barriers that satisfy a given constraint. We propose a solvency constraint similar to that in Paulsen (Finance Stoch. 4:457?C474, 2003); whenever dividends are paid out, the probability of ruin within a fixed time T and with the same strategy in the future should not exceed a predetermined level ??. It is shown how optimality can be achieved under this constraint, and numerical examples are given.     

Budget-constrained optimal reinsurance design under coherent risk measures

ABSTRACT

Reinsurance is a versatile risk management strategy commonly employed by insurers to optimize their risk profile. In this paper, we study an optimal reinsurance design problem minimizing a general law-invariant coherent risk measure of the net risk exposure of a generic insurer, in conjunction with a general law-invariant comonotonic additive convex reinsurance premium principle and a premium budget constraint. Due to its intrinsic generality, this contract design problem encompasses a wide body of optimal reinsurance models commonly encountered in practice. A three-step solution scheme is presented. Firstly, the objective and constraint functions are exhibited in the so-called Kusuoka's integral representations. Secondly, the mini-max theorem for infinite dimensional spaces is applied to interchange the infimum on the space of indemnities and the supremum on the space of probability measures. Thirdly, the recently developed Neyman–Pearson methodology due to Lo (2017a) is adopted to solve the resulting infimum problem. Analytic and transparent expressions for the optimal reinsurance policy are provided, followed by illustrative examples.     

Taxation and parental time allocation under different assumptions on altruism

This paper examines the effects of labor income taxation on parental time allocation in an OLG model in which child care arrangements, that is the combination of parental and non-parental time, matter for human capital accumulation. We show that the sign of the impact of labor income taxation on parental time with children and on growth critically depends on the assumption on the altruistic motives behind the choice of devoting time to children.     

Structural change and financing constraints

In a multi-industry growth model, firms need external funds for productivity-enhancing R&D, and face financing constraints. The cost of research differs across industries, so financing constraints hinder industry productivity growth unevenly. Equilibrium industry dynamics map into a differences-in-differences regression specification where industry growth depends on the interaction between country financial development and industry R&D intensity. The paper provides a framework for interpreting several empirical results that rely on industry growth data in terms of R&D-induced technology transfer, and identifies a new channel for finance to encourage aggregate growth: the reallocation of resources towards sectors with rapidly expanding technological frontiers.     

Financial constraints and share repurchases

We examine how the financial constraints of repurchasing firms affect their post-buyback performance. By every constraint measure we use, a set of constrained firms repurchase. They display significantly poorer post-buyback abnormal return and operating performance than unconstrained firms. Financial constraints are more important in explaining the performance of share buybacks for firms with high actual repurchase ratios. Constrained firms, especially those with high actual repurchase ratios, experience a significantly greater increase in post-buyback distress risk than unconstrained firms. Managerial hubris could explain why constrained firms buy back shares even if the buybacks do not improve shareholder wealth.     

Short-sale constraints and price bubbles

Miller (1977) demonstrated that if investors have heterogeneous beliefs and short sales are restricted, trade of a security will disproportionately reflect positive information, generating a price bubble. As this intuition applies most relevantly to short intervals of trade, a question arises as to the longevity of such a bubble. In this paper, I argue that a bubble effected by short-sale constraints persists only if agents cannot distinguish between order flow caused by positive information or order flow caused by the constraints. If the constraint is common knowledge, it should have no effect on the long-term pricing of the stock. If, however, the constraint is random and unknown, a price bubble may form.     

Financial constraints and entrepreneurial investment

There is a well documented interdependence between the investment and saving decisions of entrepreneurial households. I study this interdependence in a dynamic, general equilibrium model with heterogeneous agents and occupational choice. The simulated economy replicates U.S. data on the distribution of wealth and income, and the shares of wealth and income for each occupation. The dominant incentive behind the high level of savings of business households is the desire to relax a wealth constraint in financing entrepreneurial projects in order to operate their firms at an optimal size. Because successful firms grow over time, entrepreneurs enter business despite lower initial earnings than they would receive in paid employment.