This paper studies a non-concave optimization problem under a Value-at-Risk (VaR) or an Expected Shortfall (ES) constraint. The non-concavity of the problem stems from the non-linear payoff structure of the optimizing investor. We obtain the closed-form optimal wealth with an ES constraint as...

This paper considers a utility maximization and optimal asset allocation problem in the presence of a stochastic endowment that cannot be fully hedged through trading in the financial market. We rely on the dynamic programming approach to solve the optimization problem. The properties of the...

We introduce and solve an optimal asset allocation problem under a weighted expected shortfall (WES) constraint, which contains the risk management problem under an expected shortfall constraint of Basak and Shapiro (2001) as a special case. Furthermore, we link our risk management problem under...

We analyze an optimal consumption and investment problem for a representative agent who may have different preferences for consumption and for terminal wealth. The utility for consumption is characterized by constant relative risk aversion so consumption is always positive. In contrast, the...

This paper investigates the consumption and investment decisions of an individual facing uncertain lifespan and stochastic labor income within a Black-Scholes market framework, A key aspect of our study involves the agent's option to choose when to acquire life insurance for bequest purposes, We...

We analyze optimal asset allocation in continuous time for a collective of tied-together investors. We rely on a specific collective utility function which dates back to Karatzas (1990), by which the fund manager maximizes the weighted average of expected individual utilities for the investors...

The present paper analyzes optimal supervisory rules for pension funds taking account of diverse pension security mechanisms: support provided by either a pension guarantee fund, a plan sponsor or by both. Assuming that the regulatory rule is either to control the shortfall probability or...