Optimal investment-consumption and life insurance selection problem under inflation. A BSDE approach. (3rd April 2018)

• Record Type: Journal Article
• Authors: Guambe, Calisto; Kufakunesu, Rodwell
• Is Part Of: Optimization. Volume 67:Number 4(2018)
• Page Start: 457
• Page End: 473
• Publication Date: 2018-04-03
• Subjects: Optimal investment consumption insurance -- jump-diffusion -- inflation index -- quadratic-exponential BSDE; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1405956
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: We discuss an optimal investment, consumption and insurance problem of a wage earner under inflation. Assume a wage earner investing in a real money account and three asset prices, namely: a real zero-coupon bond, the inflation-linked real money account and a risky share described by jump-diffusion processes. Using the theory of quadratic-exponential backward stochastic differential equation (BSDE) with jumps approach, we derive the optimal strategy for the two typical utilities (exponential and power) and the value function is characterized as a solution of BSDE with jumps. Finally, we derive the explicit solutions for the optimal investment in both cases of exponential and power utility functions for a diffusion case.