Infinite horizon discounted dynamic programming subject to total variation ambiguity on conditional distribution

2016 ◽  
Author(s):  
Ioannis Tzortzis ◽  
Charalambos D. Charalambous ◽  
Themistoklis Charalambous
Keyword(s):  
Dynamic Programming ◽  
Total Variation ◽  
Conditional Distribution ◽  
Infinite Horizon ◽  
Discounted Dynamic Programming

scholarly journals Infinite Horizon Average Cost Dynamic Programming Subject to Total Variation Distance Ambiguity

2019 ◽  
Vol 57 (4) ◽  
pp. 2843-2872 ◽  
Author(s):  
Ioannis Tzortzis ◽  
Charalambos D. Charalambous ◽  
Themistoklis Charalambous
Keyword(s):  
Dynamic Programming ◽  
Total Variation ◽  
Average Cost ◽  
Infinite Horizon ◽  
Total Variation Distance ◽  
Variation Distance

Invariant problems in discounted dynamic programming

1978 ◽  
Vol 10 (2) ◽  
pp. 472-490 ◽  
Author(s):  
David Assaf
Keyword(s):  
Dynamic Programming ◽  
Arbitrary State ◽  
Transition Mechanism ◽  
Current State ◽  
A Value ◽  
Discounted Dynamic Programming ◽  
Optimal Policies ◽  
Finite Action ◽  
Value Determination ◽  
Special Case

Discounted dynamic programming problems whose transition mechanism depends only on the action taken and does not depend on the current state are considered. A value determination operation and method of obtaining optimal policies for the case of finite action space (and arbitrary state space) are presented.The solution of other problems is reduced to this special case by a suitable transformation. Results are illustrated by examples.

Constrained Discounted Dynamic Programming

1996 ◽  
Vol 21 (4) ◽  
pp. 922-945 ◽  
Author(s):  
Eugene A. Feinberg ◽  
Adam Shwartz
Keyword(s):  
Dynamic Programming ◽  
Discounted Dynamic Programming

scholarly journals On Optimal Cancellation of Policies

1977 ◽  
Vol 9 (1-2) ◽  
pp. 125-138 ◽  
Author(s):  
Hans U. Gerber
Keyword(s):  
Continuous Time ◽  
Numerical Evaluation ◽  
Infinite Horizon ◽  
Poisson Model ◽  
Analytical Form ◽  
Point Of View ◽  
Optimal Stopping Problem ◽  
The Past ◽  
Discounted Dynamic Programming ◽  
Analytical Point

One of the basic problems in life is: Given information (from the past), make decisions (that will affect the future). One of the classical actuarial examples is the adaptive ratemaking (or credibility) procedures; here the premium of a given risk is sequentially adjusted, taking into account the claims experience available when the decisions are made.In some cases, the rates are fixed and the premiums cannot be adjusted. Then the actuary faces the question: Should a given risk be underwritten in the first place, and if yes, what is the criterion (in terms of claims performance) for cancellation of the policy at a later time?Recently, Cozzolino and Freifelder [6] developed a model in an attempt to answer these questions. They assumed a discrete time, finite horizon, Poisson model. While the results lend themselves to straightforward numerical evaluation, their analytical form is not too attractive. Here we shall present a continuous time, infinite horizon, diffusion model. At the expense of being somewhat less realistic, this model is very appealing from an analytical point of view.Mathematically, the cancellation of policies amounts to an optimal stopping problem, see [8], [4], or chapter 13 in [7], and (more generally) should be viewed within the framework of discounted dynamic programming [1], [2].

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