## A stochastic optimal control problem

We can model a pension fund problem as above using a simplified version of Merton (1971)'s model of optimal portfolio selection (cf. Fleming & Rishel (1975), pp. 160-161 also Tapiero (1998)). As usual, the stock portfolio consists of two assets, one risky and the other risk free. If the price per share of the risky asset p(t) changes according to dp(t) ap(t)dt + ap(t)dw (10.1) where w is a one-dimensional standard Brownian motion, while the price q(t) per share for the risk free asset...

## Model and Analysis

Each firm i has a commercial product, Hi, which it sells for a profit. The quality of the commercial product of firm i is determined by its investment, ui. Each firm i can also contribute code, ai, to an open source. The open source product, by virtue of being open, cannot be sold and is distributed freely. However, the commercial and open source products are complementary, meaning that their sales will go hand in hand. Each firm derives quality Si from the...

## Reliability Index

University of Texas at Dallas, USA Alain-Bensoussan utdallas.edu Abstract The reliability index is a useful indicator to compute the failure probability. If J is the performance of interest and if J is a Normal random variable, the failure probability is computed by and 3 is the reliability index. When J is a nonlinear function of n normal random variables (Xi, , Xn), then the preceding formula can be generalized, with some approximation. One uses a nice property of the reliability index, to be...

## Info

Since there are conflicting terms, both stable and unstable equilibria can occur. 4. Analysis with specified functions In the first two subsections we concentrate on the implications of different specifications of our new function S (A). In Subsection 1.4.3 we specify the other functional forms as well in order to perform the complete analysis. 4.1 Exponential decay function 5 (A) As a first specification consider the following exponential function 5 (A) e lA with Y> 0 (1.16) which gives 5'...

## And Sustainable Development

Hassan Bencheckroun McGill University, Canada hassan.benchekroun staff.mcgill.ca Kobe University, Japan Corresponding author katayama rieb.kobe-u.ac.jp McGill University, Canada ngo.long staff.mcgill.ca Abstract We study an optimal control problem with a man-made capital stock, and a stock of renewable natural resource. They are substitutable inputs in the production of the final good. Starting from low levels of both stocks, the optimal policy consists of three phases. In phase I, the planner...

## Cautious policies

Notwithstanding a better yield distribution for a shortfall minimisation policy than for yield's utility maximisation, the spread of possible realisations of xu* (T) might still appear too wide for the manager to implement u*. We would argue that this might be because of no reward for superhedging xt in problem (10.10). In real life, pension fund managers will want to strongly avoid any yield below xT (as in (10.10)) but they will also enjoy yields above xT. We will want to capture this...

## Selforganized Control Of Irregular Or Perturbed Network Traffic

Dresden University of Technology, Germany Corresponding author helbing trafficforum.org Dresden University of Technology, Germany traffic stefanlaemmer.de Institut National de Recherche sur les Transports er leur S curit (INRETS), France lebacque inrets.fr Abstract We present a fluid-dynamic model for the simulation of urban traffic networks with road sections of different lengths and capacities. The model allows one to efficiently simulate the transitions between free and congested traffic,...

## References

Deforestation of Tropical Forests Economic Causes and Impact on Development. Kieler Studien, Institut fur Wel-wirtschaft an der Universitat Kiel, 241, 1992. Barbier, E.B., Burgess, J.C., and Markandya, A. The Economics of Tropical Deforestation. Ambio, 20 55-58, 1991. Barbier, E.B., and Burgess, J.C. The Economics of Forest Land Use Options. Land Economics, 73 174-195, 1997. Barbier, E.B., and Rauscher, M. Trade, Tropical Deforestation and Policy Interventions....

## Solution by Greens Theorem

An Optimal Control analysis of the optimization problem 7.4 is presented in Shani, Tsur and Zemel 2004 , where the optimal turnpike policy is derived and explained in terms of the linear dependence of the objective and state equations on the control variable x, which gives rise to the typical Most Rapid Approach Path Spence and Starrett 1975 . The similarity of this policy to the characteristic behavior derived by Sethi and coworkers for a large variety of optimization problems using Green's...

## IT 02T2

The principal parameter values are listed in Table 4.2 . For a precise meaning of these parameters, equations and variables, one refers the reader to the two books where DICE-94 and DICE-99 are explained and calibrated Nordhaus 1994 , Nordhaus and Boyer 2000 . For our purpose it suffices to say that this model captures the fundamental coupling between climate and economics growth that can be also summarized by the diagram shown in Figure 4.1 borrowed from Drouet, Edwards and Hauriex. In this...

## Volatility Forecasts And The Profitability Of Automated Trading Strategies

Department of Finance, University of Vienna, Austria Department of Finance, University of North Carolina, USA strobl unc.edu Abstract Traditional approaches to forecast option prices and implement trading strategies make use of implied volatilities. Noh, Engle, and Kane 1994 propose a different approach. Based on conditional variance models of the GARCH type they forecast volatility and use these forecasts to predict future option prices. In combination with simple trading rules Noh et al....

## And Economics

Universit de la M diterrann e, Les Milles, France A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN-10 0-387-25804-3 HB Springer Dordrecht, Berlin, Heidelberg, New York ISBN-10 0-387-25805-1 e-book Springer Dordrecht, Berlin, Heidelberg, New York ISBN-13 978-0-387-25804-1 HB Springer Dordrecht, Berlin, Heidelberg, New York ISBN-13 978-0-387-25805-8 e-book Springer Dordrecht, Berlin, Heidelberg, New York Published by Springer, P.O. Box 17, 3300 AA Dordrecht,...

## Advertising And Advertising Claims Over Time

Tapiero ESSEC, France tapiero essec.fr Abstract Advertising budget allocation with carryover effects over time is a problem that was treated extensively by economists. Additional developments were carried out by Sethi who has also provided some outstanding review papers. The model treated by Sethi were essentially defined in terms of optimal control problems using deterministic advertising models while my own were essentially sales response stochastic models with advertising budget...