Related papers: An elementary approach to the Merton problem
In this article we consider the Merton problem in a market with a single risky asset and transaction costs. We give a complete solution of the problem up to the solution of a free-boundary problem for a first-order differential equation,…
We consider the classical Merton problem of lifetime consumption-portfolio optimization problem with small proportional transaction costs. The first order term in the asymptotic expansion is explicitly calculated through a singular ergodic…
We consider a general formulation of the Principal-Agent problem with a lump-sum payment on a finite horizon, providing a systematic method for solving such problems. Our approach is the following: we first find the contract that is optimal…
We consider the classical multi-asset Merton investment problem under drift uncertainty, i.e. the asset price dynamics are given by geometric Brownian motions with constant but unknown drift coefficients. The investor assumes a prior drift…
In this paper we present a variational calculus approach to Principal-Agent problem with a lump-sum payment on finite horizon in degenerate stochastic systems, such as filtered partially observed linear systems. Our work extends the…
We study a finite horizon optimal contracting problem of a risk-neutral principal and a risk-averse agent who receives a stochastic income stream when the agent is unable to make commitments. The problem involves an infinite number of…
This paper studies the continuous time mean-variance portfolio selection problem with one kind of non-linear wealth dynamics. To deal the expectation constraint, an auxiliary stochastic control problem is firstly solved by two new…
This paper investigates the moral hazard problem in finite horizon with both continuous and lump-sum payments, involving a time-inconsistent sophisticated agent and a standard utility maximiser principal. Building upon the so-called dynamic…
In this paper, we work in the framework of the Merton problem but we impose a drawdown constraint on the consumption process. This means that consumption can never fall below a fixed proportion of the running maximum of past consumption. In…
A continuous-time consumption-investment model with constraint is considered for a small investor whose decisions are the consumption rate and the allocation of wealth to a risk-free and a risky asset with logarithmic Brownian motion…
Motivated by optimal investment problems in mathematical finance, we consider a variational problem of Neyman-Pearson type for law-invariant robust utility functionals and convex risk measures. Explicit solutions are found for…
We study a robust utility maximization problem in a general discrete-time frictionless market under quasi-sure no-arbitrage. The investor is assumed to have a random and concave utility function defined on the whole real-line. She also…
Many investment models in discrete or continuous-time settings boil down to maximizing an objective of the quantile function of the decision variable. This quantile optimization problem is known as the quantile formulation of the original…
We study the two-times differentiability of the value functions of the primal and dual optimization problems that appear in the setting of expected utility maximization in incomplete markets. We also study the differentiability of the…
We propose a simple and original approach for solving linear-quadratic mean-field stochastic control problems. We study both finite-horizon and infinite-horizon pro\-blems, and allow notably some coefficients to be stochastic. Extension to…
We study the Merton problem of optimal consumption-investment for the case of two investors sharing a final wealth. The typical example would be a husband and wife sharing a portfolio looking to optimize the expected utility of consumption…
We investigate the portfolio execution problem under a framework in which volatility and liquidity are both uncertain. In our model, we assume that a multidimensional Markovian stochastic factor drives both of them. Moreover, we model…
We propose and study a novel stochastic inertial primal-dual approach to solve composite optimization problems. These latter problems arise naturally when learning with penalized regularization schemes. Our analysis provide convergence…
The paper investigates the consumption-investment problem for an investor with Epstein-Zin utility in an incomplete market. A non-Markovian environment with unbounded parameters is considered, which is more realistic in practical financial…
We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on…