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Erscheinungsjahr: 
2023
Schriftenreihe/Nr.: 
Center for Mathematical Economics Working Papers No. 684
Verlag: 
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
Zusammenfassung: 
This paper investigates the consumption and investment decisions of an individual facing uncertain lifespan and stochastic labor income within a Black-Scholes market framework, A key aspect of our study involves the agent's option to choose when to acquire life insurance for bequest purposes, We examine two scenarios: one with a fixed bequest amount and another with a controlled bequest amount, Applying duality theory and addressing free-boundary problems, we analytically solve both cases, and provide explicit expressions for value functions and optimal strategies in both cases, In the first scenario, where the bequest amount is fixed, distinct outcomes emerge based on different levels of risk aversion parameter γ: (i) the optimal time for life insurance purchase occurs when the agent's wealth surpasses a critical threshold if γ (0,1), or (ii) life insurance should be acquired immediately if γ>1, In contrast, in the second scenario with a controlled bequest amount, regardless of γ values, immediate life insurance purchase proves to be optimal.
Schlagwörter: 
Portfolio Optimization
Consumption Planning
Life Insurance
Optimal Stopping
Stochastic Control
JEL: 
G11
E21
I13
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Dokumentart: 
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