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We investigate an optimal investment-consumption and optimal level ofinsurance on durable consumption goods with a positive loading in acontinuous-time economy. We assume that the economic agent invests in thefinancial market and in durable as well as perishable consumption goods toderive utilities from consumption over time in a jump-diffusion market.Assuming that the financial assets and durable consumption goods can be tradedwithout transaction costs, we provide a semi-explicit solution for the optimalinsurance coverage for durable goods and financial asset. With transactioncosts for trading the durable good proportional to the total value of thedurable good, we formulate the agent's optimization problem as a combinedstochastic and impulse control problem, with an implicit intervention valuefunction. We solve this problem numerically using stopping time iteration, andanalyze the numerical results using illustrative examples.

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