Size Matters, So Does Duration: The Interplay Between Offer Size and Offer Deadline

2021 ◽  
Author(s):  
Zhenyu Hu ◽  
Wenjie Tang
Keyword(s):  
Decision Analysis ◽  
Continuous Time ◽  
Optimal Strategy ◽  
Stackelberg Game ◽  
Arrival Rate ◽  
Selection Mechanism ◽  
Market Conditions ◽  
Self Selection ◽  
Private Knowledge ◽  
Exploding Offer

This paper investigates the interplay between offer size and offer deadline in a Stackelberg game involving a proposer and a responder. The proposer acts first by making an offer to the responder with a deadline, and the responder, concurrently following a continuous-time finite-horizon search for alternative offers, has to respond to the proposer’s offer by the deadline. Taking into account the responder’s reaction, the proposer’s optimal strategy can vary from an exploding offer—an offer that has to be accepted or rejected on the spot—to an offer with an extended deadline under different market conditions, proxied by characteristics of the alternative offer distribution. In particular, the proposer should offer an exploding offer when the alternative offer market is unfavorable to the responder, and the harsher it is, the smaller will be the offer size. By contrast, when the alternative offer market is favorable to the responder, the proposer can benefit from making a smaller (compared with the exploding offer) nonexploding offer, and the more favorable the market, the smaller will be the offer size and the longer the deadline. Our analysis is further extended to the case where the responder has private knowledge of the alternative offers’ arrival rate, and we characterize the optimal strategy for the proposer when she makes either a single offer or a menu of offers that serves as a self-selection mechanism. In the latter case, the optimal menu of offers can be implemented as a sign-up bonus type of contract. This paper was accepted by Manel Baucells, decision analysis.

Automated Development of Clinical Strategies Using Multistage Decision Analysis

1986 ◽  
Vol 25 (04) ◽  
pp. 207-214 ◽  
Author(s):  
P. Glasziou
Keyword(s):  
Decision Tree ◽  
Decision Analysis ◽  
Decision Trees ◽  
Optimal Strategy ◽  
Cholestatic Jaundice ◽  
Clinical Strategies ◽  
Simultaneous Study

SummaryThe development of investigative strategies by decision analysis has been achieved by explicitly drawing the decision tree, either by hand or on computer. This paper discusses the feasibility of automatically generating and analysing decision trees from a description of the investigations and the treatment problem. The investigation of cholestatic jaundice is used to illustrate the technique.Methods to decrease the number of calculations required are presented. It is shown that this method makes practical the simultaneous study of at least half a dozen investigations. However, some new problems arise due to the possible complexity of the resulting optimal strategy. If protocol errors and delays due to testing are considered, simpler strategies become desirable. Generation and assessment of these simpler strategies are discussed with examples.

scholarly journals Multi-time state mean-variance model in continuous time

2021 ◽  
Vol 27 ◽  
pp. 92
Author(s):  
Shuzhen Yang
Keyword(s):  
Boundary Conditions ◽  
Continuous Time ◽  
Optimal Strategy ◽  
Investment Portfolio ◽  
Variance Model ◽  
Investment Plan ◽  
Terminal Time ◽  
Variance Risk ◽  
Maximum Drawdown ◽  
Mean Variance

The objective of the continuous time mean-variance model is to minimize the variance (risk) of an investment portfolio with a given mean at the terminal time. However, the investor can stop the investment plan at any time before the terminal time. To solve this problem, we consider to minimize the variances of the investment portfolio in the multi-time state. The advantage of this multi-time state mean-variance model is the minimization of the risk of the investment portfolio within the investment period. To obtain the optimal strategy of the model, we introduce a sequence of Riccati equations, which are connected by jump boundary conditions. In addition, we establish the relationships between the means and variances in the multi-time state mean-variance model. Furthermore, we use an example to verify that the variances of the multi-time state can affect the average of Maximum-Drawdown of the investment portfolio.

Optimal strategies for discovering new species in continuous time

1989 ◽  
Vol 26 (04) ◽  
pp. 695-706
Author(s):  
Gerold Alsmeyer ◽  
Albrecht Irle
Keyword(s):  
New Species ◽  
Optimal Stopping ◽  
Continuous Time ◽  
Optimal Strategy ◽  
Stopping Time ◽  
Optimal Strategies ◽  
Distinct Species ◽  
Natural Generalization ◽  
General Point ◽  
Time Optimal

Consider a population of distinct species Sj , j∈J, members of which are selected at different time points T 1 , T 2,· ··, one at each time. Assume linear costs per unit of time and that a reward is earned at each discovery epoch of a new species. We treat the problem of finding a selection rule which maximizes the expected payoff. As the times between successive selections are supposed to be continuous random variables, we are dealing with a continuous-time optimal stopping problem which is the natural generalization of the one Rasmussen and Starr (1979) have investigated; namely, the corresponding problem with fixed times between successive selections. However, in contrast to their discrete-time setting the derivation of an optimal strategy appears to be much harder in our model as generally we are no longer in the monotone case. This note gives a general point process formulation for this problem, leading in particular to an equivalent stopping problem via stochastic intensities which is easier to handle. Then we present a formal derivation of the optimal stopping time under the stronger assumption of i.i.d. (X 1 , A 1) (X2, A2 ), · ·· where Xn gives the label (j for Sj ) of the species selected at Tn and An denotes the time between the nth and (n – 1)th selection, i.e. An = Tn – Tn– 1. In the case where even Xn and An are independent and An has an IFR (increasing failure rate) distribution, an explicit solution for the optimal strategy is derived as a simple consequence.

Cell loss probability for M/G/1 and time-slotted queues

2000 ◽  
Vol 37 (04) ◽  
pp. 1149-1156
Author(s):  
David McDonald ◽  
François Théberge
Keyword(s):  
Continuous Time ◽  
Time Slot ◽  
Arrival Rate ◽  
Cell Loss ◽  
Loss Probability ◽  
Finite Buffer ◽  
Asymptotic Results ◽  
Overflow Probability ◽  
The Mean

It is common practice to approximate the cell loss probability (CLP) of cells entering a finite buffer by the overflow probability (OVFL) of a corresponding infinite buffer queue, since the CLP is typically harder to estimate. We obtain exact asymptotic results for CLP and OVFL for time-slotted queues where block arrivals in different time slots are i.i.d. and one cell is served per time slot. In this case the ratio of CLP to OVFL is asymptotically (1-ρ)/ρ, where ρ is the use or, equivalently, the mean arrival rate per time slot. Analogous asymptotic results are obtained for continuous time M/G/1 queues. In this case the ratio of CLP to OVFL is asymptotically 1-ρ.

Effect of the Return Policy in a Continuous-Time Newsvendor Problem

2017 ◽  
Vol 34 (06) ◽  
pp. 1750031
Author(s):  
Weiwei Zhang ◽  
Zhongfei Li ◽  
Ke Fu ◽  
Fan Wang
Keyword(s):  
Diffusion Process ◽  
Continuous Time ◽  
Existence And Uniqueness ◽  
Stackelberg Game ◽  
Jump Diffusion ◽  
Newsvendor Problem ◽  
Stackelberg Equilibrium ◽  
Computational Results ◽  
Return Policy ◽  
Demand Rate

This paper studies the stochastic differential Stackelberg game in a continuous-time newsvendor problem with a return policy, in which one supplier sells products to one retailer and the two parties make the decisions sequentially to maximize their own expected profits. When the demand process is a general jump-diffusion process, we provide a general formula for the equilibrium if it exists. When the demand rate is an Ornstein–Uhlenbeck (O–U) process, we prove the existence and uniqueness of the equilibrium and find an explicit expression for the equilibrium. Computational results show that the return policy has significant impact on the Stackelberg equilibrium.

scholarly journals Self-selection mechanism of Fabry-Pérot micro/nanoscale wire cavity for single-mode lasing

2017 ◽  
Vol 25 (18) ◽  
pp. 21025 ◽  
Author(s):  
Yue Yang ◽  
Hua Zong ◽  
Chuang Ma ◽  
Tiantian Wei ◽  
Junchao Li ◽  
...  
Keyword(s):  
Single Mode ◽  
Selection Mechanism ◽  
Self Selection ◽  
Fabry Perot

scholarly journals The Pledging Puzzle: How Can Revocable Promises Increase Charitable Giving?

2021 ◽  
Author(s):  
James Andreoni ◽  
Marta Serra-Garcia
Keyword(s):  
Decision Analysis ◽  
Charitable Giving ◽  
Potential Usefulness ◽  
Self Selection

What is the value of pledges if they are often reneged upon? In this paper, we show—both theoretically and experimentally—that pledges can be used to screen donors and to better understand their motives for giving. In return, nonprofit managers can use the information they glean from pledges to better target future charitable giving appeals and interventions to donors, such as expressions of gratitude. In an experiment, we find that offering the option to pledge gifts induces self-selection. If expressions of gratitude are then targeted to individuals who select into pledges, reneging can be significantly reduced. Our findings provide an explanation for the potential usefulness of pledges. This paper was accepted by Yan Chen, decision analysis.

CONTINUOUS-TIME MEAN–VARIANCE OPTIMIZATION FOR DEFINED CONTRIBUTION PENSION FUNDS WITH REGIME-SWITCHING

2019 ◽  
Vol 22 (06) ◽  
pp. 1950029
Author(s):  
ZHIPING CHEN ◽  
LIYUAN WANG ◽  
PING CHEN ◽  
HAIXIANG YAO
Keyword(s):  
Brownian Motion ◽  
Portfolio Selection ◽  
Continuous Time ◽  
Optimal Strategy ◽  
Regime Switching ◽  
Efficient Frontier ◽  
Defined Contribution ◽  
Risky Assets ◽  
Mean Variance Portfolio ◽  
Mean Variance

Using mean–variance (MV) criterion, this paper investigates a continuous-time defined contribution (DC) pension fund investment problem. The framework is constructed under a Markovian regime-switching market consisting of one bank account and multiple risky assets. The prices of the risky assets are governed by geometric Brownian motion while the accumulative contribution evolves according to a Brownian motion with drift and their correlation is considered. The market state is modeled by a Markovian chain and the random regime-switching is assumed to be independent of the underlying Brownian motions. The incorporation of the stochastic accumulative contribution and the correlations between the contribution and the prices of risky assets makes our problem harder to tackle. Luckily, based on appropriate Riccati-type equations and using the techniques of Lagrange multiplier and stochastic linear quadratic control, we derive the explicit expressions of the optimal strategy and efficient frontier. Further, two special cases with no contribution and no regime-switching, respectively, are discussed and the corresponding results are consistent with those results of Zhou & Yin [(2003) Markowitz’s mean-variance portfolio selection with regime switching: A continuous-time model, SIAM Journal on Control and Optimization 42 (4), 1466–1482] and Zhou & Li [(2000) Continuous-time mean-variance portfolio selection: A stochastic LQ framework, Applied Mathematics and Optimization 42 (1), 19–33]. Finally, some numerical analyses based on real data from the American market are provided to illustrate the property of the optimal strategy and the effects of model parameters on the efficient frontier, which sheds light on our theoretical results.

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