scholarly journals Stackelberg equilibria in a continuous-time vertical contracting model with uncertain demand and delayed information

2014 ◽  
Vol 51 (A) ◽  
pp. 213-226 ◽  
Author(s):  
Bernt Øksendal ◽  
Leif Sandal ◽  
Jan Ubøe
Keyword(s):  
Continuous Time ◽  
Variable Coefficients ◽  
Uncertain Demand ◽  
Uhlenbeck Process ◽  
Delayed Information ◽  
Equilibrium Prices ◽  
Special Cases ◽  
Explicit Formulae ◽  
Contracting Model ◽  
Vertical Contracting

We consider explicit formulae for equilibrium prices in a continuous-time vertical contracting model. A manufacturer sells goods to a retailer, and the objective of both parties is to maximize expected profits. Demand is an Itô-Lévy process, and to increase realism, information is delayed. We provide complete existence and uniqueness proofs for a series of special cases, including geometric Brownian motion and the Ornstein-Uhlenbeck process, both with time-variable coefficients. Moreover, explicit solution formulae are given, so these results are operational. An interesting finding is that information that is more precise may be a considerable disadvantage for the retailer.

scholarly journals Stackelberg equilibria in a continuous-time vertical contracting model with uncertain demand and delayed information

2014 ◽  
Vol 51 (A) ◽  
pp. 213-226
Author(s):  
Bernt Øksendal ◽  
Leif Sandal ◽  
Jan Ubøe
Keyword(s):  
Continuous Time ◽  
Variable Coefficients ◽  
Uncertain Demand ◽  
Uhlenbeck Process ◽  
Delayed Information ◽  
Equilibrium Prices ◽  
Special Cases ◽  
Explicit Formulae ◽  
Contracting Model ◽  
Vertical Contracting

We consider explicit formulae for equilibrium prices in a continuous-time vertical contracting model. A manufacturer sells goods to a retailer, and the objective of both parties is to maximize expected profits. Demand is an Itô-Lévy process, and to increase realism, information is delayed. We provide complete existence and uniqueness proofs for a series of special cases, including geometric Brownian motion and the Ornstein-Uhlenbeck process, both with time-variable coefficients. Moreover, explicit solution formulae are given, so these results are operational. An interesting finding is that information that is more precise may be a considerable disadvantage for the retailer.

Dynamic Contest Games with Time Delays

2020 ◽  
Vol 22 (03) ◽  
pp. 1950017
Author(s):  
Akio Matsumoto ◽  
Ferenc Szidarovszky
Keyword(s):  
Time Scales ◽  
Characteristic Equation ◽  
Continuous Time ◽  
Local Stability ◽  
Time Delays ◽  
Delay Model ◽  
Delayed Information ◽  
Gradient Dynamics ◽  
Special Cases ◽  
Total Effort

Dynamic asymmetric contest games are examined under the assumption that the assessed value of the prize by each agent depends on the total effort of all agents, and each agent has only delayed information about the efforts of the competitors. Assuming gradient dynamics with continuous time scales, first the resulting one-delay model is investigated. Then, assuming additional delayed information about the agents’ own efforts, a two-delay model is constructed and analyzed. In both cases, first the characteristic equation is derived in the general case, and then two special cases are considered. First, symmetric agents are assumed and then general duopolies are examined. Conditions are derived for the local stability of the equilibrium including stability thresholds and stability switching curves.

Optimal Consumption and Insurance: A Continuous-time Markov Chain Approach

2008 ◽  
Vol 38 (01) ◽  
pp. 231-257 ◽  
Author(s):  
Holger Kraft ◽  
Mogens Steffensen
Keyword(s):  
Continuous Time ◽  
Optimal Solution ◽  
Decision Problems ◽  
Optimal Consumption ◽  
Continuous Time Markov Chain ◽  
Financial Decision Making ◽  
Markov Chain Approach ◽  
Special Cases ◽  
Financial Decision ◽  
The Individual

Personal financial decision making plays an important role in modern finance. Decision problems about consumption and insurance are in this article modelled in a continuous-time multi-state Markovian framework. The optimal solution is derived and studied. The model, the problem, and its solution are exemplified by two special cases: In one model the individual takes optimal positions against the risk of dying; in another model the individual takes optimal positions against the risk of losing income as a consequence of disability or unemployment.

On the Theory of Thermally Weighted Electron-Phonon Transition Probabilities

1980 ◽  
Vol 35 (9) ◽  
pp. 902-914
Author(s):  
J. Schupfner
Keyword(s):  
Transition Probabilities ◽  
Algebraic Method ◽  
Calculation Technique ◽  
Radiative Transitions ◽  
Special Cases ◽  
Explicit Formulae ◽  
The Common ◽  
Common Transition ◽  
Franck Condon ◽  
Refined Calculation

Abstract We present a refined calculation method for the phonon part (Franck-Condon Overlaps) of the transition probabilities of electron-phonon radiative and non-radiative transitions in crystals. The evaluation of the thermal averaged Franck-Condon integrals is a purely algebraic method and the transition probabilities we use are derived from first principles and completely atomistic. For the electronic transitions we take into account the frequency shift of the lattice and the change of the phonon normal coordinates. Explicit formulae of the phonon parts are derived and it is shown that the common transition probabilities used in literature are special cases of our functional calculation technique.

EXPLICIT FUNCTIONS OF FUZZY CONTROL SYSTEMS

1996 ◽  
Vol 04 (06) ◽  
pp. 515-535 ◽  
Author(s):  
LÁSZLÓ T. KÓCZY ◽  
MICHIO SUGENO
Keyword(s):  
Computational Complexity ◽  
Fuzzy Control ◽  
Control Systems ◽  
Mathematical Description ◽  
Membership Functions ◽  
Mathematical Functions ◽  
Low Computational Complexity ◽  
Special Cases ◽  
Single Input ◽  
Explicit Formulae

Fuzzy control systems have proved their applicability in many areas. Their user-friend-liness and transparency certainly belong to their main advantages, and these two enable developing and tuning such controllers easily, without knowing their exact mathematical description. Nevertheless, it is of interest to know, what mathematical functions hide behind a set of fuzzy rules and an inference machine. For practical purposes it is necessary to consider real, implementable fuzzy control systems with reasonably low computational complexity. This paper discusses the problem of what types of functions are generated by realistic fuzzy control systems. In the paper the explicit formulae of the transference functions for practically important special cases are determined, controllers having rules with triangular and trapezoidal membership functions, and crisp consequents. Here we restrict our investigations to rules with a single input.

scholarly journals Hitting Times and the Running Maximum of Markovian Growth-Collapse Processes

2011 ◽  
Vol 48 (02) ◽  
pp. 295-312 ◽  
Author(s):  
Andreas Löpker ◽  
Wolfgang Stadje
Keyword(s):  
Power Series Expansion ◽  
Inverse Function ◽  
Hitting Times ◽  
Asymptotic Results ◽  
Rapid Variation ◽  
State Dependent ◽  
Special Cases ◽  
The Laplace Transform ◽  
Running Maximum ◽  
Explicit Formulae

We consider the level hitting times τy= inf{t≥ 0 |Xt=y} and the running maximum processMt= sup{Xs| 0 ≤s≤t} of a growth-collapse process (Xt)t≥0, defined as a [0, ∞)-valued Markov process that grows linearly between random ‘collapse’ times at which downward jumps with state-dependent distributions occur. We show how the moments and the Laplace transform of τycan be determined in terms of the extended generator ofXtand give a power series expansion of the reciprocal of Ee−sτy. We prove asymptotic results for τyandMt: for example, ifm(y) = Eτyis of rapid variation thenMt/m-1(t) →w1 ast→ ∞, wherem-1is the inverse function ofm, while ifm(y) is of regular variation with indexa∈ (0, ∞) andXtis ergodic, thenMt/m-1(t) converges weakly to a Fréchet distribution with exponenta. In several special cases we provide explicit formulae.

On the GIX/G/∞ system

1990 ◽  
Vol 27 (3) ◽  
pp. 671-683 ◽  
Author(s):  
L. Liu ◽  
B. R. K. Kashyap ◽  
J. G. C. Templeton
Keyword(s):  
Steady State ◽  
Shot Noise ◽  
Continuous Time ◽  
Transient State ◽  
System Size ◽  
Noise Process ◽  
Shot Noise Process ◽  
Special Cases

By using a shot noise process, general results on system size in continuous time are given both in transient state and in steady state with discussion on some interesting results concerning special cases. System size before arrivals is also discussed.

scholarly journals Dynamic Programming and Hamilton–Jacobi–Bellman Equations on Time Scales

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yingjun Zhu ◽  
Guangyan Jia
Keyword(s):  
Dynamic Programming ◽  
Dynamic System ◽  
Time Scales ◽  
Discrete Time ◽  
Continuous Time ◽  
Stochastic Dynamic ◽  
Optimality Principle ◽  
Bellman Equations ◽  
Special Cases ◽  
Hamilton Jacobi Bellman

Bellman optimality principle for the stochastic dynamic system on time scales is derived, which includes the continuous time and discrete time as special cases. At the same time, the Hamilton–Jacobi–Bellman (HJB) equation on time scales is obtained. Finally, an example is employed to illustrate our main results.

scholarly journals Berry–Esséen bound for the parameter estimation of fractional Ornstein–Uhlenbeck processes

2019 ◽  
Vol 20 (04) ◽  
pp. 2050023 ◽  
Author(s):  
Yong Chen ◽  
Nenghui Kuang ◽  
Ying Li
Keyword(s):  
Parameter Estimation ◽  
Brownian Motion ◽  
Continuous Time ◽  
Index Formula ◽  
Hurst Index ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Time Observation ◽  
Statistical Estimations ◽  
Drift Parameter

For an Ornstein–Uhlenbeck process driven by fractional Brownian motion with Hurst index [Formula: see text], we show the Berry–Esséen bound of the least squares estimator of the drift parameter based on the continuous-time observation. We use an approach based on Malliavin calculus given by Kim and Park [Optimal Berry–Esséen bound for statistical estimations and its application to SPDE, J. Multivariate Anal. 155 (2017) 284–304].

Optimal estimation for semimartingales

1986 ◽  
Vol 23 (02) ◽  
pp. 409-417 ◽  
Author(s):  
A. Thavaneswaran ◽  
M. E. Thompson
Keyword(s):  
Continuous Time ◽  
Asymptotic Properties ◽  
Optimal Estimation ◽  
Parametric Estimation ◽  
Local Martingale ◽  
Regularity Conditions ◽  
Probability Measures ◽  
Simple Process ◽  
Special Cases ◽  
Least Squares Estimates

This paper extends a result of Godambe's theory of parametric estimation for discrete-time stochastic processes to the continuous-time case. LetP={P} be a family of probability measures such that (Ω,F, P) is complete, (Ft, t≧0) is a standard filtration, andX = (XtFt, t ≧ 0)is a semimartingale for everyP ∈ P. For a parameterθ(Ρ), supposeXt=Vt,θ+Ht,θwhere theVθprocess is predictable and locally of bounded variation and theHθprocess is a local martingale. Consider estimating equations forθof the formprocess is predictable. Under regularity conditions, an optimal form forαθin the sense of Godambe (1960) is determined. WhenVt,θis linear inθthe optimal, corresponds to certain maximum likelihood or least squares estimates derived previously in special cases. Asymptotic properties of, are discussed.

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