Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/283467 
Year of Publication: 
2023
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 684
Publisher: 
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
Abstract: 
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.
Subjects: 
Portfolio Optimization
Consumption Planning
Life Insurance
Optimal Stopping
Stochastic Control
JEL: 
G11
E21
I13
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Working Paper

Files in This Item:
File
Size
502.81 kB





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.