scholarly journals On structural properties of the value function for an unbounded jump Markov process with an application to a processor sharing retrial queue

2013 ◽  
Vol 76 (4) ◽  
pp. 425-446 ◽  
Author(s):  
S. Bhulai ◽  
A. C. Brooms ◽  
F. M. Spieksma
Keyword(s):  
Markov Process ◽  
Structural Properties ◽  
Value Function ◽  
Retrial Queue ◽  
Processor Sharing ◽  
Jump Markov Process ◽  
The Value Function

Bilevel Integer Programs with Stochastic Right-Hand Sides

2021 ◽  
Author(s):  
Junlong Zhang ◽  
Osman Y. Özaltın
Keyword(s):  
Structural Properties ◽  
Large Scale ◽  
Value Function ◽  
Integer Program ◽  
Value Functions ◽  
Integer Programs ◽  
Solution Algorithms ◽  
Right Hand ◽  
Solution Methods ◽  
The Value Function

We develop an exact value function-based approach to solve a class of bilevel integer programs with stochastic right-hand sides. We first study structural properties and design two methods to efficiently construct the value function of a bilevel integer program. Most notably, we generalize the integer complementary slackness theorem to bilevel integer programs. We also show that the value function of a bilevel integer program can be characterized by its values on a set of so-called bilevel minimal vectors. We then solve the value function reformulation of the original bilevel integer program with stochastic right-hand sides using a branch-and-bound algorithm. We demonstrate the performance of our solution methods on a set of randomly generated instances. We also apply the proposed approach to a bilevel facility interdiction problem. Our computational experiments show that the proposed solution methods can efficiently optimize large-scale instances. The performance of our value function-based approach is relatively insensitive to the number of scenarios, but it is sensitive to the number of constraints with stochastic right-hand sides. Summary of Contribution: Bilevel integer programs arise in many different application areas of operations research including supply chain, energy, defense, and revenue management. This paper derives structural properties of the value functions of bilevel integer programs. Furthermore, it proposes exact solution algorithms for a class of bilevel integer programs with stochastic right-hand sides. These algorithms extend the applicability of bilevel integer programs to a larger set of decision-making problems under uncertainty.

Double stopping by two decision-makers

1993 ◽  
Vol 25 (2) ◽  
pp. 438-452 ◽  
Author(s):  
K. Szajowski
Keyword(s):  
Markov Process ◽  
Optimal Stopping ◽  
Value Function ◽  
Optimal Strategies ◽  
Decision Makers ◽  
Secretary Problem ◽  
Gain Function ◽  
Competitive Situation ◽  
Zero Sum ◽  
The Value Function

A problem of optimal stopping of the discrete-time Markov process by two decision-makers (Player 1 and Player 2) in a competitive situation is considered. The zero-sum game structure is adopted. The gain function depends on states chosen by both decision-makers. When both players want to accept the realization of the Markov process at the same moment, the priority is given to Player 1. The construction of the value function and the optimal strategies for the players are given. The Markov chain case is considered in detail. An example related to the generalized secretary problem is solved.

On Optimal Stopping of Inhomogeneous Standard Markov Processes

1995 ◽  
Vol 2 (4) ◽  
pp. 335-346
Author(s):  
B. Dochviri
Keyword(s):  
Markov Process ◽  
Optimal Stopping ◽  
Value Function ◽  
Stopping Times ◽  
Homogeneous Markov Process ◽  
Limit Procedure ◽  
Optimal Stopping Problems ◽  
Optimal Stopping Times ◽  
The Value Function

Abstract The connection between the optimal stopping problems for inhomogeneous standard Markov process and the corresponding homogeneous Markov process constructed in the extended state space is established. An excessive characterization of the value-function and the limit procedure for its construction in the problem of optimal stopping of an inhomogeneous standard Markov process is given. The form of ε-optimal (optimal) stopping times is also found.

Double stopping by two decision-makers

1993 ◽  
Vol 25 (02) ◽  
pp. 438-452 ◽  
Author(s):  
K. Szajowski
Keyword(s):  
Markov Process ◽  
Optimal Stopping ◽  
Value Function ◽  
Optimal Strategies ◽  
Decision Makers ◽  
Secretary Problem ◽  
Gain Function ◽  
Competitive Situation ◽  
Zero Sum ◽  
The Value Function

A problem of optimal stopping of the discrete-time Markov process by two decision-makers (Player 1 and Player 2) in a competitive situation is considered. The zero-sum game structure is adopted. The gain function depends on states chosen by both decision-makers. When both players want to accept the realization of the Markov process at the same moment, the priority is given to Player 1. The construction of the value function and the optimal strategies for the players are given. The Markov chain case is considered in detail. An example related to the generalized secretary problem is solved.

The value function for time-related decisions

2011 ◽  
Author(s):  
Anouk Festjens ◽  
Siegfried Dewitte ◽  
Enrico Diecidue ◽  
Sabrina Bruyneel
Keyword(s):  
Value Function ◽  
The Value Function

scholarly journals Pricing Perpetual American Put Options with Asset-Dependent Discounting

2021 ◽  
Vol 14 (3) ◽  
pp. 130
Author(s):  
Jonas Al-Hadad ◽  
Zbigniew Palmowski
Keyword(s):  
Value Function ◽  
Asset Price ◽  
Stopping Times ◽  
Martingale Measure ◽  
Put Options ◽  
American Put Options ◽  
Exact Calculations ◽  
Negative Exponential ◽  
American Put ◽  
The Value Function

The main objective of this paper is to present an algorithm of pricing perpetual American put options with asset-dependent discounting. The value function of such an instrument can be described as VAPutω(s)=supτ∈TEs[e−∫0τω(Sw)dw(K−Sτ)+], where T is a family of stopping times, ω is a discount function and E is an expectation taken with respect to a martingale measure. Moreover, we assume that the asset price process St is a geometric Lévy process with negative exponential jumps, i.e., St=seζt+σBt−∑i=1NtYi. The asset-dependent discounting is reflected in the ω function, so this approach is a generalisation of the classic case when ω is constant. It turns out that under certain conditions on the ω function, the value function VAPutω(s) is convex and can be represented in a closed form. We provide an option pricing algorithm in this scenario and we present exact calculations for the particular choices of ω such that VAPutω(s) takes a simplified form.

scholarly journals Robo-Advising: Learning Investors’ Risk Preferences via Portfolio Choices*

2020 ◽  
Author(s):  
Humoud Alsabah ◽  
Agostino Capponi ◽  
Octavio Ruiz Lacedelli ◽  
Matt Stern
Keyword(s):  
Opportunity Cost ◽  
Value Function ◽  
Risk Preference ◽  
Portfolio Decisions ◽  
Learning Framework ◽  
Portfolio Choices ◽  
Trading Decisions ◽  
Exploration Exploitation ◽  
The Value Function ◽  
Over Time

Abstract We introduce a reinforcement learning framework for retail robo-advising. The robo-advisor does not know the investor’s risk preference but learns it over time by observing her portfolio choices in different market environments. We develop an exploration–exploitation algorithm that trades off costly solicitations of portfolio choices by the investor with autonomous trading decisions based on stale estimates of investor’s risk aversion. We show that the approximate value function constructed by the algorithm converges to the value function of an omniscient robo-advisor over a number of periods that is polynomial in the state and action space. By correcting for the investor’s mistakes, the robo-advisor may outperform a stand-alone investor, regardless of the investor’s opportunity cost for making portfolio decisions.

Metric for Disassembly and Reuse Decisions: Formulation and Validation

2008 ◽  
Author(s):  
Vijitashwa Pandey ◽  
Deborah Thurston
Keyword(s):  
Maximum Likelihood ◽  
Value Function ◽  
Choice Theory ◽  
Decision Makers ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Maximum Value ◽  
Long Range Planning ◽  
The Relationship ◽  
The Value Function

Design for disassembly and reuse focuses on developing methods to minimize difficulty in disassembly for maintenance or reuse. These methods can gain substantially if the relationship between component attributes (material mix, ease of disassembly etc.) and their likelihood of reuse or disposal is understood. For products already in the marketplace, a feedback approach that evaluates willingness of manufacturers or customers (decision makers) to reuse a component can reveal how attributes of a component affect reuse decisions. This paper introduces some metrics and combines them with ones proposed in literature into a measure that captures the overall value of a decision made by the decision makers. The premise is that the decision makers would choose a decision that has the maximum value. Four decisions are considered regarding a component’s fate after recovery ranging from direct reuse to disposal. A method on the lines of discrete choice theory is utilized that uses maximum likelihood estimates to determine the parameters that define the value function. The maximum likelihood method can take inputs from actual decisions made by the decision makers to assess the value function. This function can be used to determine the likelihood that the component takes a certain path (one of the four decisions), taking as input its attributes, which can facilitate long range planning and also help determine ways reuse decisions can be influenced.

Sign in / Sign up

Export Citation Format

Share Document