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Relaxed controls are widely used to analyze the existence of optimal controls in the literature. Though there are many optimal control problems admitting no optimal control, rare examples were shown. This paper will solve a particular optimal control problem by analyzing the optimal relaxed...
We consider a problem of finding optimal contracts in continuous time, when the agent’s actions are unobservable by the principal, who pays the agent with a one-time payoff at the end of the contract. We fully solve the case of quadratic cost and separable utility, for general utility functions....
We investigate a two-player zero-sum stochastic differential game in which the players have an asymmetric information on the random payoff. We prove that the game has a value and characterize this value in terms of dual viscosity solutions of some second order Hamilton-Jacobi equation.
We consider Bellman equations of ergodic type in first order. The Hamiltonian is quadratic on the first derivative of the solution. We study the structure of viscosity solutions and show that there exists a critical value among the solutions. It is proved that the critical value has the...
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