Optimal Control of Probability Density Functions of Stochastic Processes

Annunziato, Mario; Borzì, Alfio

doi:10.3846/1392-6292.2010.15.393-407

Cited by 67 publications

(75 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Example 3.3 Our third example is an application of RHC to the FokkerPlanck equation, first considered in [7,8]. The example differs from the first two examples in two points: first, we are now considering a controlled PDE and second, we focus on the qualitative behaviour of the solutions.…”

Section: Examplesmentioning

confidence: 99%

Approximation Properties of Receding Horizon Optimal Control

Grüne

2016

Jahresber. Dtsch. Math. Ver.

View full text Add to dashboard Cite

In this survey, receding horizon control is presented as a method for obtaining approximately optimal solutions to infinite horizon optimal control problems by iteratively solving a sequence of finite horizon optimal control problems. We investigate conditions under which we can obtain mathematically rigorous approximation results for this approach. A key ingredient of our analysis is the so-called turnpike property of optimal control problems.

show abstract

Section: Examplesmentioning

confidence: 99%

Approximation Properties of Receding Horizon Optimal Control

Grüne

2016

Jahresber. Dtsch. Math. Ver.

View full text Add to dashboard Cite

show abstract

“…It is the interest in the distribution skewness that differentiates this paper (also, that of [5] and several others cited in footnote 6) from other research in the area of dynamic portfolio management. 2 In fact, the literature tends to ignore the distribution of actual outcomes that eventuate from the optimal investment strategy.…”

Section: Introductionmentioning

confidence: 99%

“…We pursue numerical solutions in this paper, which are reliable and easy to interpret for parameter-specific problems. 5 Notwithstanding the obtained solution's parameter-specificity, our analysis can be extended to other cases through the use of specialised software (see [12]). 6 Also [13], [14], [15] and [16] .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Delivering Left-Skewed Portfolio Payoff Distributions in the Presence of Transaction Costs

Krawczyk

2015

Risks

View full text Add to dashboard Cite

For pension-savers, a low payoff is a financial disaster. Such investors will most likely prefer left-skewed payoff distributions over right-skewed payoff distributions. We explore how such distributions can be delivered. Cautious-relaxed utility measures are cautious in ensuring that payoffs don't fall much below a reference value, but relaxed about exceeding it. We find that the payoff distribution delivered by a cautious-relaxed utility measure has appealing features which payoff distributions delivered by traditional utility functions don't. In particular, cautious-relaxed distributions can have the mass concentrated on the left, hence be left-skewed. However, cautious-relaxed strategies prescribe frequent portfolio adjustments which may be expensive if transaction costs are charged. In contrast, more traditional strategies can be time-invariant. Thus we investigate the impact of transaction costs on the appeal of cautious-relaxed strategies. We find that relatively high transaction fees are required for the cautious-relaxed strategy to lose its appeal. This paper contributes to the literature which compares utility measures by the payoff distributions they produce and finds that a cautious-relaxed utility measure will deliver payoffs that many investors will prefer.

show abstract

“…The field of PDE optimization is vast, and we just mention one of many good references, [4]. A series of papers on Fokker-Planck PDE optimization has also appeared; see, e.g., [1,3]. None of these, however, deals with the boundary-based term that arises from the objective based on hitting times.…”

mentioning

confidence: 99%

Optimal Design for Estimation in Diffusion Processes from First Hitting Times

Iolov¹,

Ditlevsen²,

Longtin³

2017

SIAM/ASA J. Uncertainty Quantification

View full text Add to dashboard Cite

Abstract. We consider the optimal design problem for the Ornstein-Uhlenbeck process with fixed threshold, commonly used to describe a leaky, noisy integrate-and-fire neuron. We present a solution to the problem of devising the best external time-dependent perturbation to the process in order to facilitate the estimation of the characteristic time parameter for this process. The optimal design problem is constrained here by the fact that only the times between threshold crossings from below, known as hitting times, are observable. The optimal control is based on a maximization of the mutual information between the posterior of the unknown parameter given these observations and the distribution of the hitting times. Our approach is based on the adjoint method for computing the gradient of a functional of a solution to a Fokker-Planck partial differential equation with respect to an input function (i.e., to the control). Our method also enables the estimation of other parameters, in the case when more than one parameter is unknown.Key words. design of experiments, mutual information, leaky integrate-and-fire neuronal models, FokkerPlanck equation, probability density function control method, Ornstein-Uhlenbeck process AMS subject classifications. 62K05, 62L05, 93E20, 92C20, 92D25, 49L20, 49M25

show abstract

Optimal Control of Probability Density Functions of Stochastic Processes

Cited by 67 publications

References 26 publications

Approximation Properties of Receding Horizon Optimal Control

Approximation Properties of Receding Horizon Optimal Control

Delivering Left-Skewed Portfolio Payoff Distributions in the Presence of Transaction Costs

Optimal Design for Estimation in Diffusion Processes from First Hitting Times

Contact Info

Product

Resources

About