3,683 research outputs found
Unified Framework of Mean-Field Formulations for Optimal Multi-period Mean-Variance Portfolio Selection
The classical dynamic programming-based optimal stochastic control methods
fail to cope with nonseparable dynamic optimization problems as the principle
of optimality no longer applies in such situations. Among these notorious
nonseparable problems, the dynamic mean-variance portfolio selection
formulation had posted a great challenge to our research community until
recently. A few solution methods, including the embedding scheme, have been
developed in the last decade to solve the dynamic mean-variance portfolio
selection formulation successfully. We propose in this paper a novel mean-field
framework that offers a more efficient modeling tool and a more accurate
solution scheme in tackling directly the issue of nonseparability and deriving
the optimal policies analytically for the multi-period mean-variance-type
portfolio selection problems
Multi-period meanâvariance portfolio optimization based on Monte-Carlo simulation
We propose a simulation-based approach for solving the constrained dynamic meanâ
variance portfolio managemen tproblem. For this dynamic optimization problem, we first
consider a sub-optimal strategy, called the multi-stage strategy, which can be utilized in a
forward fashion. Then, based on this fast yet sub-optimal strategy, we propose a backward
recursive programming approach to improve it. We design the backward recursion
algorithm such that the result is guaranteed to converge to a solution, which is at leas tas
good as the one generated by the multi-stage strategy. In our numerical tests, highly
satisfactory asset allocations are obtained for dynamic portfolio management problems
with realistic constraints on the control variable
On the Exact Solution of the Multi-Period Portfolio Choice Problem for an Exponential Utility under Return Predictability
In this paper we derive the exact solution of the multi-period portfolio
choice problem for an exponential utility function under return predictability.
It is assumed that the asset returns depend on predictable variables and that
the joint random process of the asset returns and the predictable variables
follow a vector autoregressive process. We prove that the optimal portfolio
weights depend on the covariance matrices of the next two periods and the
conditional mean vector of the next period. The case without predictable
variables and the case of independent asset returns are partial cases of our
solution. Furthermore, we provide an empirical study where the cumulative
empirical distribution function of the investor's wealth is calculated using
the exact solution. It is compared with the investment strategy obtained under
the additional assumption that the asset returns are independently distributed.Comment: 16 pages, 2 figure
Arbitrage and Control Problems in Finance. Presentation.
The theory of asset pricing takes its roots in the Arrow-Debreu model (see,for instance, Debreu 1959, Chap. 7), the Black and Scholes (1973) formula,and the Cox and Ross (1976) linear pricing model. This theory and its link to arbitrage has been formalized in a general framework by Harrison and Kreps (1979), Harrison and Pliska (1981, 1983), and Du¹e and Huang (1986). In these models, security markets are assumed to be frictionless: securities can be sold short in unlimited amounts, the borrowing and lending rates are equal, and there is no transaction cost. The main result is that the price process of traded securities is arbitrage free if and only if there exists some equivalent probability measure that transforms it into a martingale, when normalized by the numeraire. Contingent claims can then be priced by taking the expected value of their (normalized) payo§ with respect to any equivalent martingale measure. If this value is unique, the claim is said to be priced by arbitrage and it can be perfectly hedged (i.e. duplicated) by dynamic trading. When the markets are dynamically complete, there is only one such a and any contingent claim is priced by arbitrage. The of each state of the world for this probability measure can be interpreted as the state price of the economy (the prices of $1 tomorrow in that state of the world) as well as the marginal utilities (for consumption in that state of the world) of rational agents maximizing their expected utility.arbitrage, control problem
Continuous-time Mean-Variance Portfolio Selection with Stochastic Parameters
This paper studies a continuous-time market {under stochastic environment}
where an agent, having specified an investment horizon and a target terminal
mean return, seeks to minimize the variance of the return with multiple stocks
and a bond. In the considered model firstly proposed by [3], the mean returns
of individual assets are explicitly affected by underlying Gaussian economic
factors. Using past and present information of the asset prices, a
partial-information stochastic optimal control problem with random coefficients
is formulated. Here, the partial information is due to the fact that the
economic factors can not be directly observed. Via dynamic programming theory,
the optimal portfolio strategy can be constructed by solving a deterministic
forward Riccati-type ordinary differential equation and two linear
deterministic backward ordinary differential equations
Application of Stochastic Optimal Control to Financial Market Debt Crises
This interdisciplinary paper explains how mathematical techniques of stochastic optimal control can be applied to the recent subprime mortgage crisis. Why did the financial markets fail to anticipate the recent debt crisis, despite the large literature in mathematical finance concerning optimal portfolio allocation and stopping rules? The uncertainty concerns the capital gain, the return on capital and the interest rate. An optimal debt ratio is derived where the drift is probabilistic but subject to economic constraints. The crises occurred because the market neglected to consider pertinent economic constraints in the dynamic stochastic optimization. The first constraint is that the firm should not be viewed in isolation. The optimizer should be the entire industry. The second economic constraint concerns the modeling of the drift of the price of the asset. The vulnerability of the borrowing firm to shocks from the capital gain, the return to capital or the interest rate, does not depend upon the actual debt/net worth per se. Instead it increases in proportion to the difference between the Actual and Optimal debt ratio, called the excess debt. A general measure of excess debt is derived and I show that it is an early warning signal of the recent crisis.stochastic optimal control, dynamic optimization, mortgage crisis, Ito equation, risk aversion, debt management, warning signals
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