A variational approach for pricing options and corporate bonds

Summary We show that option prices can always be obtained as the values of simple optimization problems. This easy remark has two consequences: sensitivity analysis is simplified (by applying the envelope theorem) and numerical procedures are improved. We give two examples of applications: options on coupon bonds and corporate bonds.     

Bunching and second-order conditions: A note on optimal tax theory

We present in this note a simple non-linear taxation model in which the agents are indexed by a one-dimensional parameter. Our purpose is to propose a method of resolution and to compute the optimal solution. We point out that the solution could not always be obtained with a simple derivation of the first-order conditions of the control problem under consideration, and we show the necessity to take into account the second-order conditions.     

Pooling and Separating Equilibria in Insurance Markets with Adverse Selection and Distribution Costs

In the Rothschild-Stiglitz [1976] model of a competitive insurance market with adverse selection, pooling equilibria cannot exist. However in practice, pooling contracts are frequent, notably in health insurance and life insurance. This is due to the fact that distribution costs are nonnegligible and increase rapidly when more contracts are offered. We modify accordingly the Rothschild-Stiglitz model by introducing such distribution costs. We find that, however small these costs may be, they entail possible existence of pooling equilibria. Moreover, in these pooling equilibria, it is the high-risk individuals who are rationed, in the sense that they would be willing to buy more insurance at the current premium/insurance ratio.     

Optimal dividend policies with random profitability

We study an optimal dividend problem under a bankruptcy constraint. Firms face a trade‐off between potential bankruptcy and extraction of profits. In contrast to previous works, general cash flow drifts, including Ornstein–Uhlenbeck and CIR processes, are considered. We provide rigorous proofs of continuity of the value function, whence dynamic programming, as well as comparison between discontinuous sub‐ and supersolutions of the Hamilton–Jacobi–Bellman equation, and we provide an efficient and convergent numerical scheme for finding the solution. The value function is given by a nonlinear partial differential equation (PDE) with a gradient constraint from below in one direction. We find that the optimal strategy is both a barrier and a band strategy and that it includes voluntary liquidation in parts of the state space. Finally, we present and numerically study extensions of the model, including equity issuance and gambling for resurrection.