Decision making with option pricing and dynamic programming: development and application

Dynamic programming (DP) is a powerful tool for solving a wide class of sequential decision-making problems under uncertainty. In principle, it enables us to compute optimal decision rules that specify the best possible decision in any situation. This article reviews developments in DP and contrasts its revolutionary impact on economics, operations research, engineering, and artificial intelligence with the comparative paucity of its real-world applications to improve the decision making of individuals and firms. The fuzziness of many real-world decision problems and the difficulty in mathematically modeling them are key obstacles to a wider application of DP in real-world settings. Nevertheless, I discuss several success stories, and I conclude that DP offers substantial promise for improving decision making if we let go of the empirically untenable assumption of unbounded rationality and confront the challenging decision problems faced every day by individuals and firms.

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An integrated neural network stochastic dynamic programming model for optimizing the operation policy of Aswan High Dam

Hydrology Research ◽

10.2166/nh.2010.043 ◽

2011 ◽

Vol 42 (1) ◽

pp. 50-67 ◽

Cited By ~ 25

Author(s):

A. H. El-Shafie ◽

M. S. El-Manadely

Keyword(s):

Neural Network ◽

Decision Making ◽

Dynamic Programming ◽

Decision Maker ◽

Stochastic Dynamic Programming ◽

Programming Model ◽

Stochastic Dynamic ◽

Release Policy ◽

Aswan High Dam ◽

Decision Making Model

Developing optimal release policies of multipurpose reservoirs is very complex, especially for reservoirs within a stochastic environment. Existing techniques are limited in their ability to represent risks associated with deciding a release policy. The risk aspect of the decisions affects the design and operation of reservoirs. A decision-making model is presented that is capable of replicating the manner in which risks associated with reservoir release decisions are perceived, interpreted and compared by a decision-maker. The model is based on Neural Network (NN) theory. This decision-making model can be used with a Stochastic Dynamic Programming (SDP) approach to produce a NN-SDP model. The resulting integrated model allows the attitudes towards risk of a decision-maker to be considered explicitly in defining the optimal release policy. Clear differences in the policies generated from the basic SDP and the NN-SDP models are observed when examining the operation of Aswan High Dam (AHD). The NN-SDP model yields policies that are more reliable and resilient and less vulnerable than those obtained using the SDP model.

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A Dynamic Programming Model for Operation Decision-Making in Bicycle Sharing Systems under a Sustainable Development Perspective

Sustainability ◽

10.3390/su9060895 ◽

2017 ◽

Vol 9 (6) ◽

pp. 895 ◽

Cited By ~ 8

Author(s):

◽

Keyword(s):

Decision Making ◽

Sustainable Development ◽

Dynamic Programming ◽

Programming Model ◽

Dynamic Programming Model ◽

Development Perspective

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DISTRIBUTION-BASED OPTION PRICING ON LATTICE ASSET DYNAMICS MODELS

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024902001572 ◽

2002 ◽

Vol 05 (06) ◽

pp. 599-618 ◽

Cited By ~ 1

Author(s):

YUJI YAMADA ◽

JAMES A. PRIMBS

Keyword(s):

Dynamic Programming ◽

Option Pricing ◽

Network Flow ◽

Stock Price ◽

Implied Volatility ◽

Market Model ◽

Flow Optimization ◽

Optimal Hedging ◽

Hedging Problem ◽

Network Flow Optimization

In this paper, we propose a numerical option pricing method based on an arbitrarily given stock distribution. We first formulate a European call option pricing problem as an optimal hedging problem by using a lattice based incomplete market model. A dynamic programming technique is then applied to solve the mean square optimal hedging problem for the discrete time multi-period case by assigning suitable probabilities on the lattice, where the underlying stock price distribution is derived directly from empirical stock price data which may possess "heavy tails". We show that these probabilities are obtained from a network flow optimization which can be solved efficiently by quadratic programming. A computational complexity analysis demonstrates that the number of iterations for dynamic programming and the number of parameters in the network flow optimization are both of square order with respect to the number of periods. Numerical experiments illustrate that our methodology generates the implied volatility smile.

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