Optimal insurance, consumption and investment decisions: a duality approach

Luís Martins, Diogo Pinheiro and Alberto A. Pinto
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Luís Martins: Universidade de Coimbra, CeBER, Faculdade de Economia
Diogo Pinheiro: Department of Mathematics, Brooklyn College of the City University of New York, and Department of Mathematics, Graduate Center of the City University of New York
Alberto A. Pinto: LIAAD–INESC TEC, Departmento de Matemática, Faculdade de Ciências, Universidade do Porto,

No 2024-05, CeBER Working Papers from Centre for Business and Economics Research (CeBER), University of Coimbra

Abstract: We employ a duality approach and martingale techniques to characterize the solutions to a stochastic optimal control problem modeling the choices available to an economic agent seeking to maximize the expected utility derived from consumption, terminal wealth, and life insurance coverage, while facing both investment risks and mortality uncertainty. The agent dynamically allocates wealth between a financial market composed of one risk-free asset and multiple risky assets, and term life insurance premiums subject, respectively, to uncertainty associated with the market conditions and the agent uncertain lifespan. Our results provide insights into the trade-offs between consumption, wealth accumulation, and life insurance demand in the presence of financial and mortality risks.

Keywords: Stochastic optimal control; Convex duality; Martingale methods; Consumption-investment problem; Life-insurance.; Stochastic optimal control; Convex duality; Martingale methods; Consumption-investment problem; Life-insurance. (search for similar items in EconPapers)
Pages: 29 pages
Date: 2024-12
New Economics Papers: this item is included in nep-rmg and nep-upt
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