1,964 research outputs found
Optimal Portfolio Liquidation for CARA Investors
We consider the finite-time optimal portfolio liquidation problem for a von Neumann-Morgenstern investor with constant absolute risk aversion (CARA). As underlying market impact model, we use the continuous-time liquidity model of Almgren and Chriss (2000). We show that the expected utility of sales revenues, taken over a large class of adapted strategies, is maximized by a deterministic strategy, which is explicitly given in terms of an analytic formula. The proof relies on the observation that the corresponding value function solves a degenerate Hamilton-Jacobi-Bellman equation with singular initial condition.Liquidity; illiquid markets; optimal liquidation strategies; dynamic trading strategies; algorithmic trading; utility maximization
Stability of the utility maximization problem with random endowment in incomplete markets
We perform a stability analysis for the utility maximization problem in a
general semimartingale model where both liquid and illiquid assets (random
endowments) are present. Small misspecifications of preferences (as modeled via
expected utility), as well as views of the world or the market model (as
modeled via subjective probabilities) are considered. Simple sufficient
conditions are given for the problem to be well-posed, in the sense the optimal
wealth and the marginal utility-based prices are continuous functionals of
preferences and probabilistic views.Comment: 21 pages, revised version. To appear in "Mathematical Finance"
Portfolio optimization in the case of an asset with a given liquidation time distribution
Management of the portfolios containing low liquidity assets is a tedious
problem. The buyer proposes the price that can differ greatly from the paper
value estimated by the seller, the seller, on the other hand, can not liquidate
his portfolio instantly and waits for a more favorable offer. To minimize
losses in this case we need to develop new methods. One of the steps moving the
theory towards practical needs is to take into account the time lag of the
liquidation of an illiquid asset. This task became especially significant for
the practitioners in the time of the global financial crises. Working in the
Merton's optimal consumption framework with continuous time we consider an
optimization problem for a portfolio with an illiquid, a risky and a risk-free
asset. While a standard Black-Scholes market describes the liquid part of the
investment the illiquid asset is sold at a random moment with prescribed
liquidation time distribution. In the moment of liquidation it generates
additional liquid wealth dependent on illiquid assets paper value. The investor
has the logarithmic utility function as a limit case of a HARA-type utility.
Different distributions of the liquidation time of the illiquid asset are under
consideration - a classical exponential distribution and Weibull distribution
that is more practically relevant. Under certain conditions we show the
existence of the viscosity solution in both cases. Applying numerical methods
we compare classical Merton's strategies and the optimal consumption-allocation
strategies for portfolios with different liquidation-time distributions of an
illiquid asset.Comment: 30 pages, 1 figur
Illiquid Assets and Optimal Portfolio Choice
The presence of illiquid assets, such as human wealth or a family owned business, complicates the problem of portfolio choice. This paper is concerned with the problem of optimal asset allocation and consumption in a continuous time model when one asset cannot be traded. This illiquid asset, which depends on an uninsurable source of risk, provides a liquid dividend. In the case of human capital we can think about this dividend as labor income. The agent is endowed with a given amount of the illiquid asset and with some liquid wealth which can be allocated in a market where there is a risky and a riskless asset. The main point of the paper is that the optimal allocations to the two liquid assets and consumption will critically depend on the endowment and characteristics of the illiquid asset, in addition to the preferences and to the liquid holdings held by the agent. We provide what we believe to be the first analytical solution to this problem when the agent has power utility of consumption and terminal wealth. We also derive the value that the agent assigns to the illiquid asset. The risk adjusted valuation procedure we develop can be used to value both liquid and illiquid assets, as well as contingent claims on those assets.
European Option Pricing with Liquidity Shocks
We study the valuation and hedging problem of European options in a market
subject to liquidity shocks. Working within a Markovian regime-switching
setting, we model illiquidity as the inability to trade. To isolate the impact
of such liquidity constraints, we focus on the case where the market is
completely static in the illiquid regime. We then consider derivative pricing
using either equivalent martingale measures or exponential indifference
mechanisms. Our main results concern the analysis of the semi-linear coupled
HJB equation satisfied by the indifference price, as well as its asymptotics
when the probability of a liquidity shock is small. We then present several
numerical studies of the liquidity risk premia obtained in our models leading
to practical guidelines on how to adjust for liquidity risk in option valuation
and hedging.Comment: 25 pages, 6 figure
- …