scholarly journals Optimal claims with fixed payoff structure

2014 ◽  
Vol 51 (A) ◽  
pp. 175-188 ◽  
Author(s):  
Carole Bernard ◽  
Ludger Rüschendorf ◽  
Steven Vanduffel
Keyword(s):  
Utility Maximization ◽  
State Dependence ◽  
Interesting Problem ◽  
Terminal Wealth ◽  
State Dependent ◽  
Additional State ◽  
Expected Utility Maximization ◽  
Payoff Structure ◽  
Continuity Assumption ◽  
Theoretical Results

Dybvig (1988) introduced the interesting problem of how to construct in the cheapest possible way a terminal wealth with desired distribution. This idea has induced a series of papers concerning generality, consequences, and applications. As the optimized claims typically follow the trend in the market, they are not useful for investors who wish to use them to protect an existing portfolio. For this reason, Bernard, Moraux, Rüschendorf and Vanduffel (2014b) imposed additional state-dependent constraints as a way of controlling the payoff structure. The present paper extends this work in various ways. In order to obtain optimal claims in general models we allow in this paper for extended contracts. We deal with general multivariate price processes and dispense with several of the regularity assumptions in the previous work (in particular, we omit any continuity assumption). State dependence is modeled by requiring terminal wealth to have a fixed copula with a benchmark wealth. In this setting, we are able to characterize optimal claims. We apply the theoretical results to deal with several hedging and expected utility maximization problems of interest.

scholarly journals Optimal claims with fixed payoff structure

2014 ◽  
Vol 51 (A) ◽  
pp. 175-188 ◽  
Author(s):  
Carole Bernard ◽  
Ludger Rüschendorf ◽  
Steven Vanduffel
Keyword(s):  
Utility Maximization ◽  
State Dependence ◽  
Interesting Problem ◽  
Terminal Wealth ◽  
State Dependent ◽  
Additional State ◽  
Expected Utility Maximization ◽  
Payoff Structure ◽  
Continuity Assumption ◽  
Theoretical Results

Dybvig (1988) introduced the interesting problem of how to construct in the cheapest possible way a terminal wealth with desired distribution. This idea has induced a series of papers concerning generality, consequences, and applications. As the optimized claims typically follow the trend in the market, they are not useful for investors who wish to use them to protect an existing portfolio. For this reason, Bernard, Moraux, Rüschendorf and Vanduffel (2014b) imposed additional state-dependent constraints as a way of controlling the payoff structure. The present paper extends this work in various ways. In order to obtain optimal claims in general models we allow in this paper for extended contracts. We deal with general multivariate price processes and dispense with several of the regularity assumptions in the previous work (in particular, we omit any continuity assumption). State dependence is modeled by requiring terminal wealth to have a fixed copula with a benchmark wealth. In this setting, we are able to characterize optimal claims. We apply the theoretical results to deal with several hedging and expected utility maximization problems of interest.

State-dependent signalling in queueing networks

1994 ◽  
Vol 26 (02) ◽  
pp. 436-455 ◽  
Author(s):  
W. Henderson ◽  
B. S. Northcote ◽  
P. G. Taylor
Keyword(s):  
Queueing Networks ◽  
State Dependence ◽  
Product Form ◽  
Batch Size ◽  
Single Server ◽  
Negative Customers ◽  
Affect Control ◽  
State Dependent ◽  
Special Cases ◽  
Equilibrium Distributions

It has recently been shown that networks of queues with state-dependent movement of negative customers, and with state-independent triggering of customer movement have product-form equilibrium distributions. Triggers and negative customers are entities which, when arriving to a queue, force a single customer to be routed through the network or leave the network respectively. They are ‘signals' which affect/control network behaviour. The provision of state-dependent intensities introduces queues other than single-server queues into the network. This paper considers networks with state-dependent intensities in which signals can be either a trigger or a batch of negative customers (the batch size being determined by an arbitrary probability distribution). It is shown that such networks still have a product-form equilibrium distribution. Natural methods for state space truncation and for the inclusion of multiple customer types in the network can be viewed as special cases of this state dependence. A further generalisation allows for the possibility of signals building up at nodes.

scholarly journals A copula-based multivariate hidden Markov model for modelling momentum in football

2021 ◽  
Author(s):  
Marius Ötting ◽  
Roland Langrock ◽  
Antonello Maruotti
Keyword(s):  
Markov Model ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
State Dependence ◽  
Change Points ◽  
Sports Fans ◽  
Modelling Framework ◽  
State Dependent ◽  
Different Levels

AbstractWe investigate the potential occurrence of change points—commonly referred to as “momentum shifts”—in the dynamics of football matches. For that purpose, we model minute-by-minute in-game statistics of Bundesliga matches using hidden Markov models (HMMs). To allow for within-state dependence of the variables, we formulate multivariate state-dependent distributions using copulas. For the Bundesliga data considered, we find that the fitted HMMs comprise states which can be interpreted as a team showing different levels of control over a match. Our modelling framework enables inference related to causes of momentum shifts and team tactics, which is of much interest to managers, bookmakers, and sports fans.

scholarly journals Reasoning about social preferences with uncertain beliefs

2021 ◽  
Author(s):  
isaac davis ◽  
Ryan W. Carlson ◽  
Yarrow Dunham ◽  
Julian Jara-Ettinger
Keyword(s):  
Expected Utility ◽  
Utility Maximization ◽  
Social Preference ◽  
Social Preferences ◽  
Social Judgments ◽  
Social Agents ◽  
Preference Reasoning ◽  
The Face ◽  
Expected Utility Maximization ◽  
Social Uncertainty

We propose a computational model of social preference judgments that accounts for the degree of an agents’ uncertainty about the preferences of others. Underlying this model is the principle that, in the face of social uncertainty, people interpret social agents’ behavior under an assumption of expected utility maximization. We evaluate our model in two experiments which each test a different kind of social preference reasoning: predicting social choices given information about social preferences, and inferring social preferences after observing social choices. The results support our model and highlight how un- certainty influences our social judgments.

DYNAMICS OF A PREY-DEPENDENT DIGESTIVE MODEL WITH STATE-DEPENDENT IMPULSIVE CONTROL

2012 ◽  
Vol 22 (04) ◽  
pp. 1250092 ◽  
Author(s):  
LINNING QIAN ◽  
QISHAO LU ◽  
JIARU BAI ◽  
ZHAOSHENG FENG
Keyword(s):  
Numerical Simulations ◽  
Analytical Method ◽  
Impulsive Control ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Period Doubling ◽  
Lambert W Function ◽  
Impulsive Effect ◽  
State Dependent ◽  
Theoretical Results

In this paper, we study the dynamical behavior of a prey-dependent digestive model with a state-dependent impulsive effect. Using the Poincaré map and the Lambert W-function, we find the analytical expression of discrete mapping. Sufficient conditions are established for transcritical bifurcation and period-doubling bifurcation through an analytical method. Exact locations of these bifurcations are explored. Numerical simulations of an example are illustrated which agree well with our theoretical results.

Specialist versus Generalist Decision Making

2018 ◽  
Author(s):  
Armin W. Schulz
Keyword(s):  
Decision Making ◽  
Expected Utility ◽  
Utility Maximization ◽  
Decision Rules ◽  
Mental States ◽  
Vast Array ◽  
Expected Utility Maximization

A number of scholars argue that human and animal decision making, at least to the extent that it is driven by representational mental states, should be seen to be the result of the application of a vast array of highly specialized decision rules. By contrast, other scholars argue that we should see human and animal representational decision making as the result of the application of a handful general principles—such as expected utility maximization—to a number of specific instances. This chapter shows that, using the results of chapters 5 and 6, it becomes possible to move this dispute forwards: the account of the evolution of conative representational decision making defended in chapter 6 together with the account of the evolution of cognitive representational decision making defended in chapter 5, makes clear that both sides of this dispute contain important insights, and that it is possible to put this entire dispute on a clearer and more precise foundation. Specifically, I show that differentially general decision rules are differentially adaptive in different circumstances: certain particular circumstances favor specialized decision making, and certain other circumstances favor more generalist decision making.

Games Embedded in Life

2020 ◽  
pp. 203-230
Author(s):  
John M. McNamara ◽  
Olof Leimar
Keyword(s):  
Reproductive Success ◽  
Dynamic Games ◽  
Traditional Approach ◽  
Holistic Approach ◽  
Current Situation ◽  
Lifetime Reproductive Success ◽  
Trade Off ◽  
State Dependent ◽  
Mean Lifetime ◽  
Payoff Structure

Many games focus on a part of the life of an organism. The payoff structure of the game then represents how the game affects fitness proxies such as mean lifetime reproductive success, which are concerned with the whole of the life of the organism. However, the traditional approach of specifying payoffs in advance of the analysis of the game can lead to inconsistencies because the rest of the life of an individual is not fixed but depends on what happens in the game. This chapter concerns this issue, identifying situations in which a more holistic approach is needed. A series of models illustrates links between the current situation and a lifetime perspective. When each of two parents must decide whether to care for their common young or desert, the payoff for desertion depends on the solution of the game and cannot be specified in advance. A game in which two males contest for a female illustrates the approach that must be taken if this game can be repeated at a later time. A game in which individuals must possess territories in order to breed is developed that highlights various interdependencies and, by incorporating learning, advances the understanding of owner–intruder interactions. The interdependencies in state-dependent dynamic games are also illustrated with a model in which individuals must trade off the risks of starvation and predation in a situation in which the choice of the best foraging habitat depends on the number of other animals that use that habitat.

Sign in / Sign up

Export Citation Format

Share Document