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

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  • Jin Sun
  • Ryle S. Perera
  • Pavel V. Shevchenko

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.

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  • Jin Sun & Ryle S. Perera & Pavel V. Shevchenko, 2019. "Optimal Investment-Consumption-Insurance with Durable and Perishable Consumption Goods in a Jump Diffusion Market," Papers 1903.00631, arXiv.org.
    • Handle: RePEc:arx:papers:1903.00631
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    References listed on IDEAS

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    3. Cuoco, Domenico & Liu, Hong, 2000. "Optimal consumption of a divisible durable good," Journal of Economic Dynamics and Control, Elsevier, vol. 24(4), pages 561-613, April.
    4. Perera, Ryle S., 2010. "Optimal consumption, investment and insurance with insurable risk for an investor in a Lévy market," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 479-484, June.
    5. Damgaard, Anders & Fuglsbjerg, Brian & Munk, Claus, 2003. "Optimal consumption and investment strategies with a perishable and an indivisible durable consumption good," Journal of Economic Dynamics and Control, Elsevier, vol. 28(2), pages 209-253, November.
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    7. Gollier, Christian & Schlesinger, Harris, 1995. " Second-Best Insurance Contract Design in an Incomplete Market," Scandinavian Journal of Economics, Wiley Blackwell, vol. 97(1), pages 123-135, March.
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