scholarly journals Game-Theoretic Optimal Portfolios for Jump Diffusions

Games ◽  
2019 ◽  
Vol 10 (1) ◽  
pp. 8 ◽  
Author(s):  
Alex Garivaltis
Keyword(s):  
Stock Prices ◽  
Continuous Time ◽  
Time Frame ◽  
Relative Performance ◽  
Jump Diffusions ◽  
Capital Growth ◽  
Game Theoretic ◽  
Capital Growth Rate ◽  
Zero Sum ◽  
Increasing Function

This paper studies a two-person trading game in continuous time that generalizes Garivaltis (2018) to allow for stock prices that both jump and diffuse. Analogous to Bell and Cover (1988) in discrete time, the players start by choosing fair randomizations of the initial dollar, by exchanging it for a random wealth whose mean is at most 1. Each player then deposits the resulting capital into some continuously rebalanced portfolio that must be adhered to over [ 0 , t ] . We solve the corresponding “investment ϕ -game”, namely the zero-sum game with payoff kernel E [ ϕ { W 1 V t ( b ) / ( W 2 V t ( c ) ) } ] , where W i is player i’s fair randomization, V t ( b ) is the final wealth that accrues to a one dollar deposit into the rebalancing rule b, and ϕ ( • ) is any increasing function meant to measure relative performance. We show that the unique saddle point is for both players to use the (leveraged) Kelly rule for jump diffusions, which is ordinarily defined by maximizing the asymptotic almost-sure continuously compounded capital growth rate. Thus, the Kelly rule for jump diffusions is the correct behavior for practically anybody who wants to outperform other traders (on any time frame) with respect to practically any measure of relative performance.

scholarly journals From time series analysis to a modified ordinary differential equation

2018 ◽  
Vol 12 (2) ◽  
pp. 85-90
Author(s):  
Meiyu Xue ◽  
Choi-Hong Lai
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Time Series ◽  
Time Series Analysis ◽  
Stock Prices ◽  
Time Frame ◽  
Equation Approach ◽  
Advantages And Disadvantages ◽  
Series Analysis ◽  
Bank Stock

In understanding Big Data, people are interested to obtain the trend and dynamics of a given set of temporal data, which in turn can be used to predict possible futures. This paper examines a time series analysis method and an ordinary differential equation approach in modeling the price movements of petroleum price and of three different bank stock prices over a time frame of three years. Computational tests consist of a range of data fitting models in order to understand the advantages and disadvantages of these two approaches. A modified ordinary differential equation model, with different forms of polynomials and periodic functions, is proposed. Numerical tests demonstrated the advantage of the modified ordinary differential equation approach. Computational properties of the modified ordinary differential equation are studied.

scholarly journals Scientific Culture and Economic Growth in the Long-Run: On a Capital Perspective

2018 ◽  
Vol 9 (1) ◽  
pp. 39
Author(s):  
Pei-xiao Qi ◽  
Nian Zheng
Keyword(s):  
Economic Growth ◽  
Growth Rate ◽  
Capital Accumulation ◽  
Human Capital Accumulation ◽  
Scientific Culture ◽  
Economic Growth Rate ◽  
Culture Capital ◽  
Long Run ◽  
Capital Growth ◽  
Capital Growth Rate

The cultural capital can be as a kind of asset that embodies, stores and produces the cultural values except for producing the economic values. With the further progress of modern civilization, scientific culture, on an economics perspective, as a combination of intangible and tangible capital, more and more becomes the one of important engine to make economic sustainable growth in the long run for a country. Based on the framework by Barro and Turnvosky, this paper constructed an economic growth model including the factor of scientific culture and mainly found that the impact of scientific culture capital growth rate on human capital accumulation is positive, and then affects economic growth rate. And the greater scientific culture capital growth rate influences the human capital accumulation, the higher economic growth rate is.

Zu M. T Aylors Analysen des Gefangenendilemmas

1982 ◽  
Vol 4 (1) ◽  
Author(s):  
Hartmut Kliemt ◽  
Bernd Schauenberg
Keyword(s):  
Repeated Games ◽  
Social Research ◽  
Social Contexts ◽  
Subsequent Paper ◽  
Social Scientists ◽  
Social Phenomena ◽  
Great Expectations ◽  
Repeated Interaction ◽  
Game Theoretic ◽  
Zero Sum

AbstractThe theory of games, though at first greeted with great expectations by some social scientists, soon became a source of frustrated hopes to many of them. Too much of the theory seemed to be devoted to “zero-sum” and “one-shot” games. But most social contexts are not zero-sum and involve repeated interaction too. There was a certain lack of such game theoretic models which could be successfully adapted to social phenomena as were apt to appear in reality. Recently the theory of games seems to be on its way to closing this gap within a special branch devoted to “repeated games” or “supergames”. Very promising is the approach of Michael Taylor which is surveyed and discussed in the subsequent paper. This approach has two main merits: First it can be understood with a modest mathematical background, secondly it can be adapted easily to a more precise reconstruction of classical topics in political theory. Though one might not agree with some of Taylor’s conclusions it seems to be worthwhile to get acquainted at least with the basics of his analysis and to take it as a first step to opening avenues for future social research.

Incomplete markets: convergence of options values under the minimal martingale measure

1999 ◽  
Vol 31 (04) ◽  
pp. 1058-1077 ◽  
Author(s):  
Jean-Luc Prigent
Keyword(s):  
Financial Market ◽  
Incomplete Markets ◽  
Stock Prices ◽  
Continuous Time ◽  
Martingale Measure ◽  
Minimal Martingale Measure ◽  
Mild Assumption ◽  
The Stability ◽  
Minimal Measure ◽  
Nikodym Derivative

In the setting of incomplete markets, this paper presents a general result of convergence for derivative assets prices. It is proved that the minimal martingale measure first introduced by Föllmer and Schweizer is a convenient tool for the stability under convergence. This extends previous well-known results when the markets are complete both in discrete time and continuous time. Taking into account the structure of stock prices, a mild assumption is made. It implies the joint convergence of the sequences of stock prices and of the Radon-Nikodym derivative of the minimal measure. The convergence of the derivatives prices follows.This property is illustrated in the main classes of financial market models.

Bias and overtaking equilibria for zero-sum continuous-time Markov games

2005 ◽  
Vol 61 (3) ◽  
pp. 437-454 ◽  
Author(s):  
Tomás Prieto-Rumeau ◽  
Onésimo Hernández-Lerma
Keyword(s):  
Continuous Time ◽  
Markov Games ◽  
Zero Sum
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