Risk-Neutral Agent

Author(s):  
Shuo Zeng ◽  
Moshe Dror
Keyword(s):  
2015 ◽  
Vol 01 (01) ◽  
pp. 1550006 ◽  
Author(s):  
Sofiene El Aoud ◽  
Frédéric Abergel

This paper presents a model for the market making of options on a liquid stock. The stock price follows a generic stochastic volatility model under the real-world probability measure [Formula: see text]. Market participants price options on this stock under a risk-neutral pricing measure [Formula: see text], and they may misspecify the parameters controlling the dynamics of the volatility process. We first consider that there is a risk-neutral agent who is willing to make markets in an option on the stock, with the aim of maximizing the expected terminal wealth at maturity. Using standard tools in optimal stochastic control, we provide analytical expressions for the optimal bid and ask quotes of the market maker. We then assume that the agent is risk-averse, and perturb the linear utility function by adding a variance term. In this setting, analytic approximations of the optimal bid and ask quotes are obtained. In the case where the stock price process follows a Heston model, Monte Carlo simulations are used to compare the optimal strategy to a "zero-intelligence" strategy, and to highlight the effects of some parameters misspecification on the performance of the strategy.


2019 ◽  
Author(s):  
Francesco Margoni ◽  
Elena Nava ◽  
Luca Surian

Most cooperative interactions involve the expectation of mutual reciprocation and are based on interpersonal trust. Thus, understanding when and how humans acquire interpersonal trust can help unveiling the origins and development of children’s cooperative behavior. Here, we investigated whether prior socio-moral information about trading partners modulates the choice of preschool- (4-5 years) and school-age children (7-8 years) to share their own goods in a child-friendly version of the Trust Game. In this game, the trustee partner can repay the child’s initial investment or keep everything and betray the trustor. In two studies, we addressed whether trust is modulated by trustees exhibiting prosocial versus antisocial behaviors (Study 1, ‘helpers and hinderers’), or respect-based versus fear-based power (Study 2, ‘leaders and bullies’). Preschoolers trusted the leader more than the bully, and trusted the hinderer less than a neutral agent, but did not yet trust the helper more than the hinderer. The tendency to trust helpers more than hinderers increased with age as a result of the increased propensity to trust the prosocial agent. In Study 3, a group of preschoolers played the Dictator Game, a measure of pure generosity, with the same agents used for Study 1. Sharing rates were reliably lower than in Study 1, suggesting that the rates of investment in the trust game cannot be due solely to altruistic or indirect reciprocity motives. Overall, these findings indicate that, by age five, children understand complex cooperative exchanges and start relying on socio-moral information when deciding whom to trust.


2007 ◽  
Author(s):  
Jian Chen ◽  
Xiaoquan Liu ◽  
Chenghu Ma
Keyword(s):  

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