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1.
Optimal payout policy in presence of downside risk 总被引:1,自引:0,他引:1
Luis H. R. Alvarez Teppo A. Rakkolainen 《Mathematical Methods of Operations Research》2009,69(1):27-58
We analyze the determination of a value maximizing dividend payout policy for a broad class of cash reserve processes modeled
as spectrally negative jump diffusions. We extend previous results based on continuous diffusion models and characterize the
value of the optimal dividend distribution strategy explicitly. We also characterize explicitly the values as well as the
optimal dividend thresholds for a class of associated optimal liquidation and sequential lump sum dividend control problems.
Our results indicate that both the value as well as the marginal value of the optimal policies are increasing functions of
policy flexibility in the discontinuous setting as well.
相似文献
2.
In this paper, we study continuous time portfolio optimization problem where individual securities are directly affected by economic factors. We consider the risk-sensitive criterion function as is familiar in the robust control literature. This is the natural setting for studying the infinite horizon case of the control problem arising in portfolio optimization. Our result extends earlier works by imposing explicitly the non-negativity constraint on the economic factors. This is achieved by using reflected diffusions. The risk-sensitive control problem with reflected diffusion is then converted into a stochastic differential game. The lower value of this game leads immediately to the desired optimal strategy. Also we prove the existence of unique strong solution to reflected diffusions with bounded measurable drift coefficient which is the first result of its kind for higher dimensional reflected diffusions. 相似文献
3.
We show that the value function of a singular stochastic
control problem is equal to the integral of the value function
of an associated optimal stopping problem. The connection is
proved for a general class of diffusions using the
method of viscosity solutions. 相似文献
4.
We show that the value function of a singular stochastic
control problem is equal to the integral of the value function
of an associated optimal stopping problem. The connection is
proved for a general class of diffusions using the
method of viscosity solutions. 相似文献
5.
Andrew N. Downes Konstantin Borovkov 《Methodology and Computing in Applied Probability》2008,10(4):621-644
We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived
for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original boundary by
a different one. In doing so we establish the existence of the first-passage time density and provide an upper bound for this
function. In the case of processes with diffusion interval equal to ℝ this is extended to a lower bound, as well as bounds
for the first crossing time of a lower boundary. An extension to some time-inhomogeneous diffusions is given. These results
are illustrated by numerical examples.
相似文献
6.
Chih-Te Yang 《TOP》2010,18(2):429-443
This study investigates a deteriorating inventory problem in which the supplier simultaneously offers the retailer either
a conditionally permissible delay in payments or a cash discount. In the case of a conditionally permissible delay, if the
retailer orders more than a predetermined quantity, then he/she has a grace period to make the full payment. Otherwise, he/she
must pay the payment for goods of certain proportion first while receiving the goods and has a grace period to pay off the
rest. As to a cash discount, if the retailer pays for the entire amount of the order within a certain short period, then he/she
will receive a cash discount from the supplier. In additions, from a financial standpoint, all cash outflows related to the
inventory control that occur at different points of time have different values. Hence, it is necessary to take account of
the factor of time value of monetary when drafting the replenishment policy. In a word, this paper uses an alternate approach-discount
cash flow (DCF) analysis to establish an inventory problem for deteriorating items in which the supplier provides the retailer
either a conditionally permissible delay or a cash discount. We then study the necessary and sufficient conditions for finding
the optimal solution. Furthermore, we establish several theoretical results to obtain the solution that provides the smallest
present value of all future cash flows. Finally, several numerical examples are given to illustrate the results and obtain
some managerial insights. 相似文献
7.
This paper is concerned with the stochastic optimal control problem of jump diffusions. The relationship between stochastic
maximum principle and dynamic programming principle is discussed. Without involving any derivatives of the value function,
relations among the adjoint processes, the generalized Hamiltonian and the value function are investigated by employing the
notions of semijets evoked in defining the viscosity solutions. Stochastic verification theorem is also given to verify whether
a given admissible control is optimal. 相似文献
8.
9.
We study two classes of stochastic control problems with semicontinuous cost: the Mayer problem and optimal stopping for controlled diffusions. The value functions are introduced via linear optimization problems on appropriate sets of probability measures. These sets of constraints are described deterministically with respect to the coefficient functions. Both the lower and upper semicontinuous cases are considered. The value function is shown to be a generalized viscosity solution of the associated HJB system, respectively, of some variational inequality. Dual formulations are given, as well as the relations between the primal and dual value functions. Under classical convexity assumptions, we prove the equivalence between the linearized Mayer problem and the standard weak control formulation. Counter-examples are given for the general framework. 相似文献
10.
本文研究了一维扩散过程的最优停止问题,论证了W iener过程和几何布朗运动是F e ller过程,同时给出了一般扩散过程的处理方法. 相似文献
11.
12.
Sören Christensen Fabián Crocce Ernesto Mordecki Paavo Salminen 《Stochastic Processes and their Applications》2019,129(7):2561-2581
This paper develops an approach for solving perpetual discounted optimal stopping problems for multidimensional diffusions, with special emphasis on the -dimensional Wiener process. We first obtain some verification theorems for diffusions, based on the Green kernel representation of the value function. Specializing to the multidimensional Wiener process, we apply the Martin boundary theory to obtain a set of tractable integral equations involving only harmonic functions that characterize the stopping region of the problem in the bounded case. The approach is illustrated through the optimal stopping problem of a -dimensional Wiener process with a positive definite quadratic form reward function. 相似文献
13.
For a class of global optimization (maximization) problems, with a separable non-concave objective function and a linear constraint a computationally efficient heuristic has been developed.The concave relaxation of a global optimization problem is introduced. An algorithm for solving this problem to optimality is presented. The optimal solution of the relaxation problem is shown to provide an upper bound for the optimal value of the objective function of the original global optimization problem. An easily checked sufficient optimality condition is formulated under which the optimal solution of concave relaxation problem is optimal for the corresponding non-concave problem. An heuristic algorithm for solving the considered global optimization problem is developed.The considered global optimization problem models a wide class of optimal distribution of a unidimensional resource over subsystems to provide maximum total output in a multicomponent systems.In the presented computational experiments the developed heuristic algorithm generated solutions, which either met optimality conditions or had objective function values with a negligible deviation from optimality (less than 1/10 of a percent over entire range of problems tested). 相似文献
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15.
《Indagationes Mathematicae》2023,34(5):1181-1205
We consider the impulse control of Lévy processes under the infinite horizon, discounted cost criterion. Our motivating example is the cash management problem in which a controller is charged a fixed plus proportional cost for adding to or withdrawing from his/her reserve, plus an opportunity cost for keeping any cash on hand. Our main result is to provide a verification theorem for the optimality of control band policies in this scenario. We also analyze the transient and steady-state behavior of the controlled process under control band policies and explicitly solve for an optimal policy in the case in which the Lévy process to be controlled is the sum of a Brownian motion with drift and a compound Poisson process with exponentially distributed jump sizes. 相似文献
16.
We consider the optimal control of a multidimensional cash management system where the cash balances fluctuate as a homogeneous diffusion process in Rn. We formulate the model as an impulse control problem on an unbounded domain with unbounded cost functions. Under general assumptions we characterize the value function as a weak solution of a quasi-variational inequality in a weighted Sobolev space and we show the existence of an optimal policy. Moreover we prove the local uniform convergence of a finite element scheme to compute numerically the value function and the optimal cost. We compute the solution of the model in two-dimensions with linear and distance cost functions, showing what are the shapes of the optimal policies in these two simple cases. Finally our third numerical experiment computes the solution in the realistic case of the cash concentration of two bank accounts made by a centralized treasury. 相似文献
17.
We introduce a class of continuous planar processes, called “semimartingales on rays”, and develop for them a change-of-variable formula involving quite general classes of test functions. Special cases of such processes are diffusions which choose, once at the origin, the rays for their subsequent voyage according to a fixed probability measure in the manner of Walsh (1978). We develop existence and uniqueness results for these “Walsh diffusions”, study their asymptotic behavior, and develop tests for explosions in finite time. We use these results to find an optimal strategy, in a problem of stochastic control with discretionary stopping involving Walsh diffusions. 相似文献
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19.
《European Journal of Operational Research》2006,170(1):72-90
The major purpose of this paper is to apply a stochastic single-period inventory management approach to analyze optimal cash management policies with fuzzy cash demand based on fuzzy integral method so that total cost is minimized. We will find that, after defuzzification, the cash-raising amounts and the total costs between the fuzzy case and the crisp case are slightly different when the variation of cash demand is small. As a result, we point out that the fuzzy stochastic single-period model is one extension of the crisp models. In any case, one may conclude that a conscientious analysis in fuzzy mathematics like that presented in this paper provides a financial decision maker with a deeper insight into the more real cash management problem. 相似文献
20.
First exit time distributions for multidimensional processes are key quantities in many areas of risk management and option pricing. The aim of this paper is to provide a flexible, fast and accurate algorithm for computing the probability of the first exit time from a bounded domain for multidimensional diffusions. First, we show that the probability distribution of this stopping time is the unique (weak) solution of a parabolic initial and boundary value problem. Then, we describe the algorithm which is based on a combination of the sparse tensor product finite element spaces and an hp-discontinuous Galerkin method. We illustrate our approach with several examples. We also compare the numerical results to classical Monte Carlo methods. 相似文献