7,715 research outputs found
Optimal Investment with Transaction Costs and Stochastic Volatility
Two major financial market complexities are transaction costs and uncertain
volatility, and we analyze their joint impact on the problem of portfolio
optimization. When volatility is constant, the transaction costs optimal
investment problem has a long history, especially in the use of asymptotic
approximations when the cost is small. Under stochastic volatility, but with no
transaction costs, the Merton problem under general utility functions can also
be analyzed with asymptotic methods. Here, we look at the long-run growth rate
problem when both complexities are present, using separation of time scales
approximations. This leads to perturbation analysis of an eigenvalue problem.
We find the first term in the asymptotic expansion in the time scale parameter,
of the optimal long-term growth rate, and of the optimal strategy, for fixed
small transaction costs.Comment: 27 pages, 4 figure
Optimal Dynamic Basis Trading
We study the problem of dynamically trading a futures contract and its
underlying asset under a stochastic basis model. The basis evolution is modeled
by a stopped scaled Brownian bridge to account for non-convergence of the basis
at maturity. The optimal trading strategies are determined from a utility
maximization problem under hyperbolic absolute risk aversion (HARA) risk
preferences. By analyzing the associated Hamilton-Jacobi-Bellman equation, we
derive the exact conditions under which the equation admits a solution and
solve the utility maximization explicitly. A series of numerical examples are
provided to illustrate the optimal strategies and examine the effects of model
parameters.Comment: 27 pages, 10 figure
Moral Hazard in Dynamic Risk Management
We consider a contracting problem in which a principal hires an agent to
manage a risky project. When the agent chooses volatility components of the
output process and the principal observes the output continuously, the
principal can compute the quadratic variation of the output, but not the
individual components. This leads to moral hazard with respect to the risk
choices of the agent. We identify a family of admissible contracts for which
the optimal agent's action is explicitly characterized, and, using the recent
theory of singular changes of measures for It\^o processes, we study how
restrictive this family is. In particular, in the special case of the standard
Homlstr\"om-Milgrom model with fixed volatility, the family includes all
possible contracts. We solve the principal-agent problem in the case of CARA
preferences, and show that the optimal contract is linear in these factors: the
contractible sources of risk, including the output, the quadratic variation of
the output and the cross-variations between the output and the contractible
risk sources. Thus, like sample Sharpe ratios used in practice, path-dependent
contracts naturally arise when there is moral hazard with respect to risk
management. In a numerical example, we show that the loss of efficiency can be
significant if the principal does not use the quadratic variation component of
the optimal contract.Comment: 36 pages, 3 figure
Portfolio Choice with Stochastic Investment Opportunities: a User's Guide
This survey reviews portfolio choice in settings where investment
opportunities are stochastic due to, e.g., stochastic volatility or return
predictability. It is explained how to heuristically compute candidate optimal
portfolios using tools from stochastic control, and how to rigorously verify
their optimality by means of convex duality. Special emphasis is placed on
long-horizon asymptotics, that lead to particularly tractable results.Comment: 31 pages, 4 figure
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