A stochastic differential game for optimal investment of an insurer with regime switching

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dc.contributor.authorElliott, R.
dc.contributor.authorSiu, T.
dc.date.issued2011
dc.description.abstractWe introduce a model to discuss an optimal investment problem of an insurance company using a game theoretic approach. The model is general enough to include economic risk, financial risk, insurance risk, and model risk. The insurance company invests its surplus in a bond and a stock index. The interest rate of the bond is stochastic and depends on the state of an economy described by a continuous-time, finite-state, Markov chain. The stock index dynamics are governed by a Markov, regime-switching, geometric Brownian motion modulated by the chain. The company receives premiums and pays aggregate claims. Here the aggregate insurance claims process is modeled by either a Markov, regime-switching, random measure or a Markov, regime-switching, diffusion process modulated by the chain. We adopt a robust approach to model risk, or uncertainty, and generate a family of probability measures using a general approach for a measure change to incorporate model risk. In particular, we adopt a Girsanov transform for the regime-switching Markov chain to incorporate model risk in modeling economic risk by the Markov chain. The goal of the insurance company is to select an optimal investment strategy so as to maximize either the expected exponential utility of terminal wealth or the survival probability of the company in the ‘worst-case’ scenario. We formulate the optimal investment problems as two-player, zero-sum, stochastic differential games between the insurance company and the market. Verification theorems for the HJB solutions to the optimal investment problems are provided and explicit solutions for optimal strategies are obtained in some particular cases.
dc.description.statementofresponsibilityRobert J. Elliott and Tak Kuen Siu
dc.identifier.citationQuantitative Finance, 2011; 11(3):365-380
dc.identifier.doi10.1080/14697681003591704
dc.identifier.issn1469-7688
dc.identifier.issn1469-7696
dc.identifier.urihttp://hdl.handle.net/2440/68497
dc.language.isoen
dc.publisherIOP Publishing Ltd.
dc.relation.grantARC
dc.rights© 2011 Taylor & Francis
dc.source.urihttps://doi.org/10.1080/14697681003591704
dc.subjectOptimal investment
dc.subjectInsurance company
dc.subjectMarkov regime-switching models
dc.subjectModel uncertainty
dc.subjectInsurance claim process
dc.subjectStochastic differential games
dc.subjectExponential utility
dc.subjectSurvival probability
dc.subjectDynamic programming
dc.subjectHJB equations
dc.titleA stochastic differential game for optimal investment of an insurer with regime switching
dc.typeJournal article
pubs.publication-statusPublished

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