12 research outputs found
Portfolio Optimization under Partial Information with Expert Opinions: a Dynamic Programming Approach
This paper investigates optimal portfolio strategies in a market where the
drift is driven by an unobserved Markov chain. Information on the state of this
chain is obtained from stock prices and expert opinions in the form of signals
at random discrete time points. As in Frey et al. (2012), Int. J. Theor. Appl.
Finance, 15, No. 1, we use stochastic filtering to transform the original
problem into an optimization problem under full information where the state
variable is the filter for the Markov chain. The dynamic programming equation
for this problem is studied with viscosity-solution techniques and with
regularization arguments.Comment: 31 page
Expert Opinions and Logarithmic Utility Maximization in a Market with Gaussian Drift
This paper investigates optimal portfolio strategies in a financial market
where the drift of the stock returns is driven by an unobserved Gaussian mean
reverting process. Information on this process is obtained from observing stock
returns and expert opinions. The latter provide at discrete time points an
unbiased estimate of the current state of the drift. Nevertheless, the drift
can only be observed partially and the best estimate is given by the
conditional expectation given the available information, i.e., by the filter.
We provide the filter equations in the model with expert opinion and derive in
detail properties of the conditional variance. For an investor who maximizes
expected logarithmic utility of his portfolio, we derive the optimal strategy
explicitly in different settings for the available information. The optimal
expected utility, the value function of the control problem, depends on the
conditional variance. The bounds and asymptotic results for the conditional
variances are used to derive bounds and asymptotic properties for the value
functions. The results are illustrated with numerical examples.Comment: 21 page
Portfolio Optimization under Partial Information with Expert Opinions
This paper investigates optimal portfolio strategies in a market with partial information
on the drift. The drift is modelled as a function of a continuous-time Markov chain
with finitely many states which is not directly observable. Information on the drift is
obtained from the observation of stock prices. Moreover, expert opinions in the form
of signals at random discrete time points are included in the analysis. We derive the
filtering equation for the return process and incorporate the filter into the state variables
of the optimization problem. This problem is studied with dynamic programming
methods. In particular, we propose a policy improvement method to obtain computable
approximations of the optimal strategy. Numerical results are presented at the end. (author's abstract
Optimal portfolios with bounded shortfall risks
This paper considers dynamic optimal portfolio strategies of utility maximizing
investors in the presence of risk constraints. In particular, we investigate the optimization problem with an additional constraint modeling bounded shortfall risk
measured by Value at Risk or Expected Loss. Using the Black-Scholes model of a
complete financial market and applying martingale methods we give analytic expressions for the optimal terminal wealth and the optimal portfolio strategies and
present some numerical results
Optimal portfolios with bounded shortfall risks
This paper considers dynamic optimal portfolio strategies of utility maximizing
investors in the presence of risk constraints. In particular, we investigate the optimization problem with an additional constraint modeling bounded shortfall risk
measured by Value at Risk or Expected Loss. Using the Black-Scholes model of a
complete financial market and applying martingale methods we give analytic expressions for the optimal terminal wealth and the optimal portfolio strategies and
present some numerical results
Dynamic optimal portfolios benchmarking the stock market
The paper investigates dynamic optimal portfolio strategies of utility maximizing portfolio managers in the presence of risk constraints. Especially we consider
the risk, that the terminal wealth of the portfolio falls short of a certain benchmark level which is proportional to the stock price. This risk is measured by the
Expected Utility Loss. We generalize the findings our previous papers to this case.
Using the Black-Scholes model of a complete financial market and applying martingale methods, analytic expressions for the optimal terminal wealth and the optimal
portfolio strategies are given. Numerical examples illustrate the analytic results
PORTFOLIO OPTIMIZATION UNDER PARTIAL INFORMATION WITH EXPERT OPINIONS
This paper investigates optimal portfolio strategies in a market with partial information on the drift. The drift is modelled as a function of a continuous-time Markov chain with finitely many states which is not directly observable. Information on the drift is obtained from the observation of stock prices. Moreover, expert opinions in the form of signals at random discrete time points are included in the analysis. We derive the filtering equation for the return process and incorporate the filter into the state variables of the optimization problem. This problem is studied with dynamic programming methods. In particular, we propose a policy improvement method to obtain computable approximations of the optimal strategy. Numerical results are presented at the end.Portfolio optimization, hidden Markov model, dynamic programming