Stochastic differential game, Esscher transform and general equilibrium under a Markovian regime-switching lévy model

Yang Shen, Tak Kuen Siu*

*Corresponding author for this work

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

In this paper, we discuss three different approaches to select an equivalent martingale measure for the valuation of contingent claims under a Markovian regime-switching Lévy model. These approaches are the game theoretic approach, the Esscher transformation approach and the general equilibrium approach. We employ the dynamic programming principle to derive the optimal strategies and the value functions in the stochastic differential game and the general equilibrium approaches, each of which lead to an equivalent martingale measure. We also compare equivalent martingale measures chosen by the three approaches. Under certain conditions, the equivalent martingale measures chosen by the stochastic differential game and the Esscher transformation approaches coincide. If the equity premium is in its equilibrium state, the equivalent martingale measures chosen by the Esscher transformation and the general equilibrium approaches are identical.

Original languageEnglish
Pages (from-to)757-768
Number of pages12
JournalInsurance: Mathematics and Economics
Volume53
Issue number3
DOIs
Publication statusPublished - Nov 2013

Keywords

  • Lévy process
  • regime-switching
  • HJB equation
  • Stochastic differential game
  • Esscher transform
  • general equilibrium
  • equivalent martingale measure

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