Optimal Investment-Consumption-Insurance with Durable and Perishable Consumption Goods in a Jump Diffusion Market

24 Pages Posted: 25 Mar 2019

See all articles by Jin Sun

Jin Sun

University of Technology Sydney (UTS)

Ryle Perera

Macquarie University

Pavel V. Shevchenko

Macquarie University - Department of Actuarial Studies and Business Analytics

Date Written: March 1, 2019

Abstract

We investigate an optimal investment-consumption and optimal level of insurance on durable consumption goods with a positive loading in a continuous-time economy. We assume that the economic agent invests in the financial market and in durable as well as perishable consumption goods to derive utilities from consumption over time in a jump-diffusion market. Assuming that the financial assets and durable consumption goods can be traded without transaction costs, we provide a semi-explicit solution for the optimal insurance coverage for durable goods and financial asset. With transaction costs for trading the durable good proportional to the total value of the durable good, we formulate the agent's optimization problem as a combined stochastic and impulse control problem, with an implicit intervention value function. We solve this problem numerically using stopping time iteration, and analyze the numerical results using illustrative examples.

Keywords: optimal stochastic control, durable goods, jump-diffusion market, insurance, optimal impulse control, intervention value, stopping time iteration

Suggested Citation

Sun, Jin and Perera, Ryle and Shevchenko, Pavel V., Optimal Investment-Consumption-Insurance with Durable and Perishable Consumption Goods in a Jump Diffusion Market (March 1, 2019). Available at SSRN: https://ssrn.com/abstract=3345428 or http://dx.doi.org/10.2139/ssrn.3345428

Jin Sun

University of Technology Sydney (UTS) ( email )

15 Broadway, Ultimo
PO Box 123
Sydney, NSW 2007
Australia

Ryle Perera

Macquarie University ( email )

North Ryde
Sydney, New South Wales 2109
Australia
98508578 (Phone)

Pavel V. Shevchenko (Contact Author)

Macquarie University - Department of Actuarial Studies and Business Analytics ( email )

Australia

HOME PAGE: http://www.mq.edu.au/research/centre-for-risk-analytics/pavel-shevchenko

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