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 the 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 PDE with a gradient constraint from below in one dimension. 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 credit lines

Viscosity solutions for controlled McKean--Vlasov jump-diffusions

We study a class of non linear integro-differential equations on the Wasserstein space related to the optimal control of McKean--Vlasov jump-diffusions. We develop an intrinsic notion of viscosity solutions that does not rely on the lifting to an Hilbert space and prove a comparison theorem for these solutions. We also show that the value function is the unique viscosity solution

Firm dynamics depend on cash and capital

We study how costly financing and bankruptcy interact with a firm's cash and capital to determine optimal investment, payout, issuance, and default. The dynamic model connects disperse strands of the empirical literature, and we find support in the data for novel non-linearities: (1) equity issuance scaled by capital is declining and convex in capital and (2) payout scaled by capital is concave in capital. Accounting for these predictions in prior studies increases explanatory power and alters results. We prove uniqueness of the model solution by proving a comparison theorem for discontinuous viscosity solutions.https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3975014First author draf

Investment and consumption with small transaction costs

This thesis consists of two parts, both of which study the infinite horizon Merton problem under asymptotically small transaction costs. In the first part the asymptotical no trade regions are found numerically for proportional transaction costs, whereas the second is an initial attempt to employ homogenization theory previously used for fixed and proportional costs separately to the case of both costs simultaneously