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Optimal Dividend Payout with Bankruptcy Risk
Optimal Dividend Payout with Bankruptcy Risk
We study the optimal dividend policy for an insurance company with shareholders exhibiting constant absolute risk aversion (CARA). The firm faces bankruptcy risk, and we model its reserves using a Cramér-Lundberg process, approximated by Brownian motion. We solve the resulting stochastic control problem numerically and analyze the probability of ruin under optimal the strategy.
Optimal Consumption Portfolio Choice with Stochastic Volatility
Optimal Consumption Portfolio Choice with Stochastic Volatility
We study an optimal consumption and investment problem under Epstein-Zin preferences in a stochastic volatility setting. Using a finite difference method, we numerically solve the associated Hamilton-Jacobi-Bellman (HJB) equation and analyze the impact of the elasticity of intertemporal substitution (EIS) and return-volatility correlation on optimal strategies.
Optimal Consumption Portfolio Choice with Stochastic Interest Rates
Optimal Consumption Portfolio Choice with Stochastic Interest Rates
This paper addresses the optimal consumption and bond investment problem under Epstein-Zin preferences in the presence of stochastic interest rates. We employ a finite difference method to numerically solve the corresponding Hamilton-Jacobi-Bellman (HJB) equation and examine how varying the elasticity of intertemporal substitution (EIS) influences investor behavior.
Continuous-Time Principal-Agent Models
Continuous-Time Principal-Agent Models
This study replicates the continuous-time principal–agent model of Sannikov (2008). We formulate the incentive-compatible optimal contracting problem with moral hazard and solve it numerically using an implicit finite-difference scheme applied to the associated Hamilton–Jacobi–Bellman (HJB) equation. The replication confirms the original model’s results for the baseline case (optimal retirement of the agent at an endogenously determined threshold) and demonstrates how outcomes change when the agent can quit, be replaced, or be trained (promoted) to higher productivity. Under each scenario, we compute the principal’s value function and optimal effort and consumption policies.
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