This paper presents a critique of expected utility theory as a descriptive model of decision making under risk, and develops an alternative model, called prospect theory. Choices among risky prospects exhibit several pervasive effects that are inconsistent with the basic tenets of utility theory. In particular, people underweight outcomes that are merely probable in comparison with outcomes that are obtained with certainty. This tendency, called the certainty effect, contributes to risk aversion in choices involving sure gains and to risk seeking in choices involving sure losses. In addition, people generally discard components that are shared by all prospects under consideration. This tendency, called the isolation effect, leads to inconsistent preferences when the same choice is presented in different forms. An alternative theory of choice is developed, in which value is assigned to gains and losses rather than to final assets and in which probabilities are replaced by decision weights. The value function is normally concave for gains, commonly convex for losses, and is generally steeper for losses than for gains. Decision weights are generally lower than the corresponding probabilities, except in the range of low probabilities. Overweighting of low probabilities may contribute to the attractiveness of both insurance and gambling.

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A controller continuously monitors a storage system, such as an Inventory or bank account, whose content Z = {Zt, t > 01 fluctuates 2 as a (p,a ) Brownian motion in the absence of control. Holding costs are incurred continuously at rate h(Zt). At any time, the controller may instantaneously increase the content of the system, incurring a proporitional cost of r times the size of the increase, or decrease the content at a cost of I times the size of the decrease. We consider the case where h is convex on a finite interval [a,R] and h = -outside this interval. The objective is to minimize the expected discounted sum of holding costs and control costs over an Infinite planning horizon.It is shown that there exists an optimal control limit policy, characterized by two parameters a and b (a < a < b < P). Roughly speaking, this policy exerts the minimum amounts of control sufficient to keep Zt c [a,b] for all t > 0. Put another way, the optimal control limit policy imposes on Z a lower reflecting barrier at a and an upper reflecting barrier at b. We do not give a full-blown El algorithm for construction of the optimal control limits, but a computational scheme could easily be developed from our constructive proof of existence. Z t = Xt+R t-t t > 0,and we define the associated cost function . t' k(x) =E ff e-t h(Z)dt +r e-Y dR~ t i eYt dL 0 0with the Riemann-Stieltjes integrals on the right defined to include the control costs rR 0 and AL 0 incurred at t = 0 (see 13). Our objective is to find a policy which minimizes k(x) for every starting state x.An essential feature of this problem is that the controller can instantaneously change the content (or state) of the storage system.Thus, it is possible to further impose state constraints on the controller's actions, which may be formally expressed by setting h(x) = -for some states x. In the same way, one of the controller's options may be eliminated by setting r = -or IThe special case where r <, A < -and In this paper we consider the Instantaneous control problem with r < -, A < and a holding cost function of the formwhere --< a < 0 < -. It will be shown that there exists an optimal control limit policy with lower limit a and upper limit b, where a < a < b < P. We do not present a full-blown algorithm for computation of the optimal control limits a and b, but a computational scheme could easily be developed from our constructive proof of existence. Our treatment generalizes the result by Harrison and Taylor(6] described earlier, and the methods used here are also more elegant and more general in their applicability. This improvement in methodology and presentation has itself been a major goal In our study, although the extension to general convex holding costs Is potentially important for applications.It will ultimately be found that the minimal cost function f for our instantaneous control problem satsifies the optimality Heuristic Derivation of the Optimality EquationTo simplify discussion, we assume In this section that h(x) < for all x eIR (the real line),...

The paper represents a model for financial valuation of a firm which has control of the dividend payment stream and its risk as well as potential profit by choosing different business activities among those available to it. This model extends the classical Miller-Modigliani theory of firm valuation to the situation of controllable business activities in a stochastic environment. We associate the value of the company with the expected present value of the net dividend distributions (under the optimal policy). Copyright Blackwell Publishers 1999.

We apply regenerative theory to derive certain relations between steady state probabilities of a Markov chain. These relations are then used to develop a numerical algorithm to find these probabilities. The algorithm is a modification of the Gauss-Jordan method, in which all elements used in numerical computations are nonnegative; as a consequence, the algorithm is numerically stable.

This paper deals with the dividend optimization problem for a financial or an insurance entity which can control its business activities, simultaneously reducing the risk and potential profits. It also controls the timing and the amount of dividends paid out to the shareholders. The objective of the corporation is to maximize the expected total discounted dividends paid out until the time of bankruptcy. Due to the presence of a fixed transaction cost, the resulting mathematical problem becomes a mixed classical-impulse stochastic control problem. The analytical part of the solution to this problem is reduced to quasivariational inequalities for a second-order nonlinear differential equation. We solve this problem explicitly and construct the value function together with the optimal policy. We also compute the expected time between dividend payments under the optimal policy.

We consider a financial market model with two assets. One has deterministic rate of growth, while the rate of growth of the second asset is governed by a Brownian motion with drift. We can shift money from one asset to another; however, there are losses of money (brokerage fees) involved in shifting money from the risky to the nonrisky asset. We want to maximize the expected rate of growth of funds. It is proved that an optimal policy keeps the ratio of funds in risky and nonrisky assets within a certain interval with minimal effort.

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