A variational inequality for a partially observed stopping time problem

2005 ◽  
pp. 472-480 ◽  
Author(s):  
Michael Kohlmann ◽  
Raymond Rishel
Keyword(s):  
Variational Inequality ◽  
Stopping Time ◽  
Time Problem ◽  
Partially Observed

Approximations of the optimal stopping problem in partial observation

1986 ◽  
Vol 23 (2) ◽  
pp. 341-354 ◽  
Author(s):  
G. Mazziotto
Keyword(s):  
Optimal Stopping ◽  
Measure Space ◽  
Stopping Time ◽  
Optimal Stopping Problem ◽  
Snell Envelope ◽  
Infinite Dimensional ◽  
Markov State ◽  
State Process ◽  
Partially Observed ◽  
True State

The resolution of the optimal stopping problem for a partially observed Markov state process reduces to the computation of a function — the Snell envelope — defined on a measure space which is in general infinite-dimensional. To avoid these computational difficulties, we propose in this paper to approximate the optimal stopping time as the limit of times associated to similar problems for a sequence of processes converging towards the true state. We show on two examples that these approximating states can be chosen such that the Snell envelopes can be explicitly computed.

Optimal double stopping time problem

2010 ◽  
Vol 348 (1-2) ◽  
pp. 65-69
Author(s):  
Magdalena Kobylanski ◽  
Marie-Claire Quenez ◽  
Elisabeth Rouy-Mironescu
Keyword(s):  
Stopping Time ◽  
Time Problem

scholarly journals Optimal stopping time problem in a general framework

2012 ◽  
Vol 17 (0) ◽  
Author(s):  
Magdalena Kobylanski ◽  
Marie-Claire Quenez
Keyword(s):  
Optimal Stopping ◽  
General Framework ◽  
Stopping Time ◽  
Optimal Stopping Time ◽  
Time Problem

scholarly journals A Simple GDP-based Model for Public Investments at Risk

2017 ◽  
Vol 8 (1) ◽  
pp. 91-114
Author(s):  
Bernard Lapeyre ◽  
Emile Quinet
Keyword(s):  
Cost Benefit Analysis ◽  
Investment Decision ◽  
Decision Rules ◽  
Stopping Time ◽  
Cost Benefit ◽  
Cost Ratio ◽  
Public Authorities ◽  
Public Investments ◽  
Time Problem ◽  
Wide Range

Investment decision rules in risk situations have been extensively analyzed for firms. Most research focus on financial options and the wide range of methods based on dynamic programming currently used by firms to decide on whether and when to implement an irreversible investment under uncertainty. The situation is quite different for public investments, which are decided and largely funded by public authorities. These investments are assessed by public authorities, not through market criteria, but through public Cost-Benefit Analysis (CBA) procedures. Strangely enough, these procedures pay little attention to risk and uncertainty. The present text aims at filling this gap. We address the classic problem of whether and when an investment should be implemented. This stopping time problem is established in a framework where the discount rate is typically linked toGDP, which follows a Brownian motion, and where the benefits and cost of implementation follow linked Brownian motions. We find that the decision rule depends on a threshold value of the First Year Advantage/Cost ratio. This threshold can be expressed in a closed form including the means, standard deviations and correlations of the stochastic variables. Simulations with sensible current values of these parameters show that the systemic risk, coming from the correlation between the benefits of the investment and economic growth, is not that high, and that more attention should be paid to risks relating to the construction cost of the investment; furthermore, simple rules of thumb are designed for estimating the above-mentioned threshold. Some extensions are explored. Others are suggested for further research.

On a discretization procedure for the stopping time problem

Stochastics ◽  
1984 ◽  
Vol 11 (3-4) ◽  
pp. 213-236 ◽  
Author(s):  
Hiroaki Morimoto
Keyword(s):  
Stopping Time ◽  
Time Problem ◽  
Discretization Procedure

scholarly journals Optimal Reinsurance Problem under Fixed Cost and Exponential Preferences

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 295
Author(s):  
Matteo Brachetta ◽  
Claudia Ceci
Keyword(s):  
Optimal Stopping ◽  
Risk Model ◽  
Stopping Time ◽  
Fixed Cost ◽  
Model Parameters ◽  
Insurance Company ◽  
Optimal Reinsurance ◽  
Retention Level ◽  
Step Procedure ◽  
Time Problem

We investigate an optimal reinsurance problem for an insurance company taking into account subscription costs: that is, a constant fixed cost is paid when the reinsurance contract is signed. Differently from the classical reinsurance problem, where the insurer has to choose an optimal retention level according to some given criterion, in this paper, the insurer needs to optimally choose both the starting time of the reinsurance contract and the retention level to apply. The criterion is the maximization of the insurer’s expected utility of terminal wealth. This leads to a mixed optimal control/optimal stopping time problem, which is solved by a two-step procedure: first considering the pure-reinsurance stochastic control problem and next discussing a time-inhomogeneous optimal stopping problem with discontinuous reward. Using the classical Cramér–Lundberg approximation risk model, we prove that the optimal strategy is deterministic and depends on the model parameters. In particular, we show that there exists a maximum fixed cost that the insurer is willing to pay for the contract activation. Finally, we provide some economical interpretations and numerical simulations.

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