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Optimal investment-consumption-insurance with partial information

  • Hiroaki HataEmail author
Original Paper
  • 27 Downloads

Abstract

We consider an optimal investment, consumption, and life insurance purchase problem for a wage earner. We treat a stochastic factor model that the mean returns of risky assets depend linearly on underlying economic factors formulated as the solutions of linear stochastic differential equations. We discuss the partial information case that the wage earner can not observe the factor process and use only past information of risky assets. Then, our problem is formulated as a stochastic control problem with partial information. Applying the dynamic programming principle, we derive a coupled system of the Hamilton–Jacobi–Bellman (HJB) equation and two backward stochastic differential equations (BSDEs), and obtain the explicit solution. Finally, we strictly prove the verification theorem, and construct the optimal investment-consumption-insurance strategy.

Keywords

Optimal investment-consumption-insurance HARA utility Stochastic factor model Partial information Hamilton–Jacobi–Bellman equation Backward stochastic differential equation 

Mathematics Subject Classification

49L20 91E28 91E30 93E11 93E20 60H10 60H30 

Notes

Acknowledgements

The authors would like to thank the referees for helpful comments and suggestions.

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Copyright information

© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of EducationShizuoka UniversityShizuokaJapan

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