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Time-inconsistent stochastic optimal control problems in insurance and finance

Łukasz Delong
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Łukasz Delong: Warsaw School of Economics SGH, Collegium of Economic Analysis, Division of Probabilistic Methods

Collegium of Economic Analysis Annals, 2018, issue 51, 229-254

Abstract: In this paper we study time-inconsistent stochastic optimal control problems. We discuss the assumption of time-consistency of the optimal solution and its fundamental relation with Bellman equation. We point out consequences of time-inconsistency of the optimal solution and we explain the concept of Nash equilibrium which allows us to handle the time-inconsistency. We describe an extended Hamilton-Jacobi-Bellman equation which can be used to derive an equilibrium strategy in a time-inconsistent stochastic optimal control problem. We give three examples of time-inconsistent dynamic optimization problems which can arise in insurance and finance. We present the solution for exponential utility maximization problem with wealth-dependent risk aversion.

Keywords: Bellman equation; Nash equilibrium; time-inconsistency; wealth-dependent risk aversion (search for similar items in EconPapers)
Date: 2018
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Handle: RePEc:sgh:annals:i:51:y:2018:p:229-254