Production and portfolio choice under jump–diffusion productivity shocks

How should an entrepreneur jointly allocate capital across production inputs and invest in financial markets when productivity is subject to rare discrete shocks? We formulate this as a stochastic control problem that reduces explicitly to a static risk-adjusted profit maximization, with a closed-form value function and consumption rule under both constant absolute risk aversion (CARA) and constant relative risk aversion (CRRA) preferences. The risk-adjusted cost encodes three nonadditive interactions: a hedging demand linking production and portfolio decisions through productivity-return correlation, a variance penalty on correlated input holdings, and a jump correction that penalizes large positions because discrete productivity losses cannot be hedged through liquidation. Jump risk and productivity-return correlation amplify each other, so partial models systematically underestimate total risk costs. Firms exposed to supply disruptions, financial crises, or technological shifts should therefore treat input allocation as a portfolio problem, not a purely technological one.