# Optimal consumption policies in illiquid markets

@article{Cretarola2008OptimalCP, title={Optimal consumption policies in illiquid markets}, author={Alessandra Cretarola and Fausto Gozzi and Huy{\^e}n Pham and Peter Tankov}, journal={Finance and Stochastics}, year={2008}, volume={15}, pages={85-115} }

We investigate optimal consumption policies in the liquidity risk model introduced by Pham and Tankov (Math. Finance 18:613–627, 2008). Our main result is to derive smoothness C1 results for the value functions of the portfolio/consumption choice problem. As an important consequence, we can prove the existence of the optimal control (portfolio/consumption strategy) which we characterize both in feedback form in terms of the derivatives of the value functions and as the solution of a second…

## 16 Citations

### Investment/Consumption Problem in Illiquid Markets with Regime-Switching

- Economics, MathematicsSIAM J. Control. Optim.
- 2014

The dynamic programming method is used to provide the characterization of the value function of this stochastic control problem in terms of the unique viscosity solution to a system of integro-partial differential equations, which allows the existence of optimal investment/consumption strategies characterized in feedback forms.

### Illiquidity Effects in Optimal Consumption-Investment Problems

- Economics
- 2010

We study the effect of liquidity freezes on an economic agent optimizing her utility of consumption in a perturbed Black-Scholes-Merton model. The single risky asset follows a geometric Brownian…

### Viscosity Characterization of the Value Function of an Investment-Consumption Problem in Presence of an Illiquid Asset

- Mathematics, EconomicsJ. Optim. Theory Appl.
- 2014

The main goal of the paper is the characterization of the value function as unique viscosity solution of an associated Hamilton–Jacobi–Bellman equation, and using such a result to build a numerical algorithm, allowing one to approximate thevalue function and so to measure the cost of illiquidity.

### Viscosity Characterization of the Value Function of an Investment-Consumption Problem in Presence of an Illiquid Asset

- Mathematics, EconomicsJournal of Optimization Theory and Applications
- 2013

We study a problem of optimal investment/consumption over an infinite horizon in a market consisting of a liquid and an illiquid asset. The liquid asset is observed and can be traded continuously,…

### IMPACT OF TIME ILLIQUIDITY IN A MIXED MARKET WITHOUT FULL OBSERVATION

- Mathematics, Economics
- 2012

We study a problem of optimal investment/consumption over an infinite horizon in a market with two possibly correlated assets: one liquid and one illiquid. The liquid asset is observed and can be…

### Optimal investment on finite horizon with random discrete order flow in illiquid markets

- Economics
- 2009

This work proves the convergence of the optimal performance, when the deterministic intensity of the order flow approaches infinity at any time, to the optimal expected utility for an investor trading continuously in a perfectly liquid market model with no-short sale constraints.

### Mean-Variance portfolio selection in presence of infrequently traded stocks

- EconomicsEur. J. Oper. Res.
- 2014

### Optimal consumption/investment problem with light stocks: A mixed continuous-discrete time approach

- BusinessAppl. Math. Comput.
- 2012

### Optimal Consumption of a Generalized Geometric Brownian Motion with Fixed and Variable Intervention Costs

- Economics, Mathematics
- 2013

We consider the problem of maximizing expected lifetime utility from consumption of a generalized geometric Brownian motion in the presence of controlling costs with a fixed component. Under general…

### Optimal Stopping Problems in Lévy Models with Random Observations

- MathematicsActa Applicandae Mathematicae
- 2018

In the standard optimal stopping problems, actions are artificially restricted to the moments of observations of costs or benefits. In the standard experimentation and learning models based on…

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