The optimal portfolio problem for a bank account, single risky stock and a rolling horizon bond is developed. The stochastic short-term interest rate with the Cox-Ingersoll-Ross (CIR) dynamics affects the prices of th...
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The optimal portfolio problem for a bank account, single risky stock and a rolling horizon bond is developed. The stochastic short-term interest rate with the Cox-Ingersoll-Ross (CIR) dynamics affects the prices of the stock and rolling horizon bond. The investment objective is maximizing expected CRRA utility of terminal wealth. The problem has been solved by the stochastic dynamic programming principle and the completion of squares technique. The closed-form optimal trading strategy is obtained. A numerical example illustrating the results is presented.
We consider a capacity planning optimization problem in a general theoretical framework that extends the classical Erlang loss modeland related stochastic loss networks to support time-varying workloads. The time hori...
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ISBN:
(纸本)9781595936394
We consider a capacity planning optimization problem in a general theoretical framework that extends the classical Erlang loss modeland related stochastic loss networks to support time-varying workloads. The time horizon consists of a sequence of coarse time intervals, each of which involves a stochastic loss network under a fixed multi-class workload that can change in a general manner from one interval to the next. The optimization problem consists of determining the capacities for each time interval that maximize a utility function over the entire time horizon, finite or infinite, where rewards gained from servicing customers are offset by penalties associated with deploying capacities in an interval and with changing capacities among intervals. We derive a state-dependent optimal policy within the context of a particular limiting regime of the optimization problem, and we prove this solution to be a symptotically optimal. Then, under fairly mild conditions, we prove that a similar structural property holds for the optimal solution of the original stochastic optimization problem, and we show how the optimal capacities comprising this solution can be efficiently computed.
We present a new approach to pricing American-style derivatives that is applicable to any Markovian setting (i.e., not limited to geometric Brownian motion) for which European call-option prices are readily available....
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We present a new approach to pricing American-style derivatives that is applicable to any Markovian setting (i.e., not limited to geometric Brownian motion) for which European call-option prices are readily available. By approximating the value function with an appropriately chosen interpolation function, the pricing of an American-style derivative with arbitrary payoff function is converted to the pricing of a portfolio of European call options, leading to analytical expressions for those cases where analytical European call prices are available (e.g., the Merton jump-diffusion process). Furthermore, in many settings, the approach yields upper and lower analytical bounds that provably converge to the true option price. We provide computational results to illustrate the convergence and accuracy of the resulting estimators.
This paper studies the problem of the existence of stationary optimal policies for finite state controlled Markov chains, with compact action space and imperfect observations, under the long-run average cost criterion...
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This paper studies the problem of the existence of stationary optimal policies for finite state controlled Markov chains, with compact action space and imperfect observations, under the long-run average cost criterion. It presents sufficient conditions for existence of solutions to the associated dynamicprogramming equation, that strengthen past results. There is a detailed discussion comparing the different assumptions commonly found in the literature. (c) 2005 Elsevier B.V. All rights reserved.
This paper develops a discretized version of a stochastic model of the economic growth and studies its convergence and stability properties. A nonlinear model of the economic growth, which involves the production, tec...
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This paper develops a discretized version of a stochastic model of the economic growth and studies its convergence and stability properties. A nonlinear model of the economic growth, which involves the production, technology stock, and their rates as the main variables, is considered. We analyze the case where the production function does not satisfy the Inada conditions and we show that, in this case, a sufficient condition for the existence of a unique steady state is that the marginal utility function should possess a horizontal and vertical asymptotic elasticity.
This paper considers a class of multi-period flexible supply policies with options and capacity constraints. The main results are to characterize the optimal ordering and purchasing options policy and the minimum expe...
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This paper considers a class of multi-period flexible supply policies with options and capacity constraints. The main results are to characterize the optimal ordering and purchasing options policy and the minimum expected cost in a period and thereafter under the assumptions about the options and ordering quantities. (c) 2005 Elsevier B.V. All rights reserved.
This paper concerns two families of Markov decision problem that fall within the family of (bi-directional) restless bandits, an intractable class of decision processes introduced by Whittle. The spinning plates probl...
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This paper concerns two families of Markov decision problem that fall within the family of (bi-directional) restless bandits, an intractable class of decision processes introduced by Whittle. The spinning plates problem concerns the optimal management of a portfolio of reward-generating assets whose yields grow with investment but otherwise tend to decline. In the model of asset exploitation called the squad system, the yield from an asset tends to decline when it is used but will recover when the asset is at rest. In all cases, simply stated conditions are given that guarantee indexability of the problem, together with conditions necessary and sufficient for its strict indexability. The index heuristics for asset activation that emerge from the analysis are assessed numerically and found to perform very strongly.
We present a deterministic model that specifies lane direction in a multi-laned bridge that has a movable barrier that divides the two directions of traffic flow, in order to reduce congestion. A probabilistic dynamic...
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We present a deterministic model that specifies lane direction in a multi-laned bridge that has a movable barrier that divides the two directions of traffic flow, in order to reduce congestion. A probabilistic dynamicprogramming formulation for a stochastic extension of the model is also presented. Analysis of the special structure of the dynamicprogramming formulation provides new insights into important aspects of certain traffic planning problems and represents a useful addition to the traffic network planner's toolkit. A case study involving the lane direction management of an actual bridge is also provided.
作者：
Gharbi, AKenné, JPHajji, AUniv Quebec
Ecole Technol Super Automated Prod Engn Dept Prod Syst Design & Control Lab Montreal PQ H3C 1K3 Canada Univ Quebec
Ecole Technol Super Dept Mech Engn Montreal PQ H3C 1K3 Canada
This paper deals with the control of the production rates and set-up actions of an unreliable multiple-machine, multiple-product manufacturing system. Each part type can be processed for a specified period on one of t...
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This paper deals with the control of the production rates and set-up actions of an unreliable multiple-machine, multiple-product manufacturing system. Each part type can be processed for a specified period on one of the involved machines. When switching the production from one type to another, each machine requires both set-up time and set-up cost. Our objective is to determine the production rates and a sequence of set-ups in order to minimize the total set-up and surplus cost. As an analytical or even a numerical solution of the problem is very difficult to find, a combined approach is presented. The proposed approach is based on stochastic optimal control theory, discrete event simulation, experimental design and response surface methodology. It is proved experimentally that an extended version of the Hedging Corridor Policy is more realistic and guarantees better performance for two study cases. The first consists of the unreliable one-machine case facing exponential failure and repair time distribution. The second, which is more complex and where the optimal control theory may not be easily used to obtain the optimal control policy, consists of five machines facing non-exponential failure and repair time distributions. To illustrate the contribution of the paper and the robustness of the obtained control policy, numerical examples and sensitivity analysis are presented.
The Markovian optimal policies are studied for the problem of economic inventory control or resource management in a finite time horizon. Under some conditions, in particular, when the prices are stochastic and there ...
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The Markovian optimal policies are studied for the problem of economic inventory control or resource management in a finite time horizon. Under some conditions, in particular, when the prices are stochastic and there is a positive fixed setup cost K, the existence of {S, s}-type Markovian optimal management policies is proved. When K = 0, the optimal policies are of (S)-type, in which case a comparison is made between the optimal policies under stochastic and deterministic prices. It turns out that under stochastic prices the optimal policies should be more conservative in order to maximize the present value of expected revenue. (c) 2004 Elsevier B.V. All rights reserved.
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