scholarly journals On Optimal Leader’s Investments Strategy in a Cyclic Model of Innovation Race with Random Inventions Times

Games ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 52
Author(s):  
Sergey M. Aseev ◽  
Masakazu Katsumoto
Keyword(s):  
Stochastic Process ◽  
Driving Force ◽  
Time Horizon ◽  
Optimization Problem ◽  
Technology Spillovers ◽  
Infinite Time ◽  
Cyclic Model ◽  
Stochastic Optimization Problem ◽  
Optimal Investments ◽  
Poisson Type

In this paper, we develop a new dynamic model of optimal investments in R&D and manufacturing for a technological leader competing with a large number of identical followers on the market of a technological product. The model is formulated in the form of the infinite time horizon stochastic optimization problem. The evolution of new generations of the product is treated as a Poisson-type cyclic stochastic process. The technology spillovers effect acts as a driving force of technological change. We show that the original probabilistic problem that the leader is faced with can be reduced to a deterministic one. This result makes it possible to perform analytical studies and numerical calculations. Numerical simulations and economic interpretations are presented as well.

scholarly journals Logarithmic Asymptotics for Probability of Component-Wise Ruin in a Two-Dimensional Brownian Model

Risks ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 83 ◽  
Author(s):  
Krzysztof Dȩbicki ◽  
Lanpeng Ji ◽  
Tomasz Rolski
Keyword(s):  
Time Horizon ◽  
Optimization Problem ◽  
Adjustment Coefficient ◽  
Two Dimensional ◽  
Infinite Time ◽  
Initial Capital ◽  
Brownian Motion With Drift ◽  
Surplus Process ◽  
Logarithmic Asymptotics ◽  
Brownian Model

We consider a two-dimensional ruin problem where the surplus process of business lines is modelled by a two-dimensional correlated Brownian motion with drift. We study the ruin function P ( u ) for the component-wise ruin (that is both business lines are ruined in an infinite-time horizon), where u is the same initial capital for each line. We measure the goodness of the business by analysing the adjustment coefficient, that is the limit of - ln P ( u ) / u as u tends to infinity, which depends essentially on the correlation ρ of the two surplus processes. In order to work out the adjustment coefficient we solve a two-layer optimization problem.

OPTIMAL PORTFOLIO AND CONSUMPTION MODELS UNDER LOSS AVERSION IN INFINITE TIME HORIZON

2016 ◽  
Vol 30 (4) ◽  
pp. 553-575 ◽  
Author(s):  
Jingjing Song ◽  
Xiuchun Bi ◽  
Shuguang Zhang
Keyword(s):  
Loss Aversion ◽  
Time Horizon ◽  
Optimization Problem ◽  
Optimal Portfolio ◽  
Reference Level ◽  
Optimal Consumption ◽  
Martingale Method ◽  
Infinite Time ◽  
Closed Form Solutions ◽  
Infinite Time Horizon

This paper investigates continuous-time optimal portfolio and consumption problems under loss aversion in an infinite time horizon. The investor's goal is to choose the optimal portfolio and consumption policies to maximize total discounted S-shaped utility from consumption. The problems are solved under two different situations respectively for the reference level: exogenous or endogenous. For the case of exogenous reference level, which is independent of the consumption policy, the optimal consumption policy and wealth process are obtained through the martingale method and replicating technique. For the case of endogenous reference level, which is related to the past actual consumption, the optimization problem with stochastic reference level is first transformed into an equivalent optimization problem with zero reference point, the corresponding relationship between them is proved, and then the relevant optimal consumption policy and wealth process are also obtained. When the investment opportunity sets are constants, the closed-form solutions of the portfolio and consumption policies are derived under two different situations respectively.

scholarly journals Nonlinear evolution problems with singular coefficients in the lower order terms

2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Fernando Farroni ◽  
Luigi Greco ◽  
Gioconda Moscariello ◽  
Gabriella Zecca
Keyword(s):  
Lower Order ◽  
Time Horizon ◽  
Existence Result ◽  
Nonlinear Evolution ◽  
Order Term ◽  
Time Behavior ◽  
Infinite Time ◽  
Singular Coefficient ◽  
Singular Coefficients ◽  
Lower Order Terms

AbstractWe consider a Cauchy–Dirichlet problem for a quasilinear second order parabolic equation with lower order term driven by a singular coefficient. We establish an existence result to such a problem and we describe the time behavior of the solution in the case of the infinite–time horizon.

Unique Open Loop Nash Equilibria on the Infinite Time Horizon

2001 ◽  
Vol 34 (20) ◽  
pp. 29-34
Author(s):  
Gerhard Jank ◽  
Dirk Kremer ◽  
Gábor Kun
Keyword(s):  
Time Horizon ◽  
Nash Equilibria ◽  
Open Loop ◽  
Infinite Time ◽  
Infinite Time Horizon

scholarly journals An inventory model for deteriorating items under time varying demand condition

2013 ◽  
Vol 8 (1) ◽  
pp. 1273-1278
Author(s):  
Srichandan Mishra ◽  
S.P. Mishra ◽  
N. Mishra ◽  
J. Panda
Keyword(s):  
Time Horizon ◽  
Cost Minimization ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Time Varying ◽  
Infinite Time ◽  
Infinite Time Horizon ◽  
Demand Rate ◽  
Demand Condition ◽  
Varying Demand

In this paper we discuss the development of an inventory model for deteriorating items which investigates an instantaneous replenishment model for the items under cost minimization. A time varying type of demand rate with infinite time horizon, exponential deterioration and with shortage in considered. The result is illustrated with numerical example.

Singular Perturbation Based Solution to Optimal Microalgal Growth Problem and Its Infinite Time Horizon Analysis

2010 ◽  
Vol 55 (3) ◽  
pp. 767-772 ◽  
Author(s):  
Sergej Celikovsky ◽  
Stepan Papacek ◽  
Alejandro Cervantes-Herrera ◽  
Javier Ruiz-Leon
Keyword(s):  
Singular Perturbation ◽  
Time Horizon ◽  
Infinite Time ◽  
Infinite Time Horizon ◽  
Growth Problem
Sign in / Sign up

Export Citation Format

Share Document