🤖 AI Summary
This paper examines the optimal investment, consumption, and insurance decisions of an infinitely-lived economic agent who consumes both perishable and durable goods. The agent allocates wealth across a risk-free asset, a risky asset, and a durable good whose price follows a correlated jump-diffusion process; the durable good depreciates deterministically and is subject to insurable Poisson shocks, hedged via a loading-fee insurance contract. Methodologically, the study innovatively incorporates durable-good insurance into a continuous-time stochastic control framework, formulating a hybrid model combining stochastic and impulse controls to characterize optimal insurance coverage, portfolio allocation, and consumption under transaction costs. Analytically, a semi-closed-form solution is derived in the absence of transaction costs. Numerical simulations reveal that transaction costs substantially widen the insurance gap and fundamentally reshape the asset allocation frontier.
📝 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.
