Motivated by financial and empirical arguments and in order to introduce a more flexible methodology of pricing,we provide a new approach to asset pricing based on Backward Volterra equations.The approach relies on an...Motivated by financial and empirical arguments and in order to introduce a more flexible methodology of pricing,we provide a new approach to asset pricing based on Backward Volterra equations.The approach relies on an arbitrage-free and incomplete market setting in continuous time by choosing non-unique pricing measures depending either on the time of evaluation or on the maturity of payoffs.We show that in the latter case the dynamics can be captured by a time-delayed backward stochastic Volterra integral equation here introduced which,to the best of our knowledge,has not yet been studied.We then prove an existence and uniqueness result for time-delayed backward stochastic Volterra integral equations.Finally,we present a Lucas-type consumption-based asset pricing model that justifies the emergence of stochastic discount factors matching the term structure of Sharpe ratios.展开更多
In the context of risk measures,the capital allocation problem is widely studied in the literature where different approaches have been developed,also in connection with cooperative game theory and systemic risk.Altho...In the context of risk measures,the capital allocation problem is widely studied in the literature where different approaches have been developed,also in connection with cooperative game theory and systemic risk.Although static capital allocation rules have been extensively studied in the recent years,only few works deal with dynamic capital allocations and its relation with BSDEs.Moreover,all those works only examine the case of an underneath risk measure satisfying cash-additivity and,moreover,a large part of them focuses on the specific case of the gradient allocation where Gateaux differentiability is assumed.The main goal of this paper is,instead,to study general dynamic capital allocations associated to cash-subadditive risk measures,generalizing the approaches already existing in the literature and motivated by the presence of(ambiguity on)interest rates.Starting from an axiomatic approach,we then focus on the case where the underlying risk measures are induced by BSDEs whose drivers depend also on the yvariable.In this setting,we surprisingly find that the corresponding capital allocation rules solve special kinds of Backward Stochastic Volterra Integral Equations(BSVIEs).展开更多
文摘Motivated by financial and empirical arguments and in order to introduce a more flexible methodology of pricing,we provide a new approach to asset pricing based on Backward Volterra equations.The approach relies on an arbitrage-free and incomplete market setting in continuous time by choosing non-unique pricing measures depending either on the time of evaluation or on the maturity of payoffs.We show that in the latter case the dynamics can be captured by a time-delayed backward stochastic Volterra integral equation here introduced which,to the best of our knowledge,has not yet been studied.We then prove an existence and uniqueness result for time-delayed backward stochastic Volterra integral equations.Finally,we present a Lucas-type consumption-based asset pricing model that justifies the emergence of stochastic discount factors matching the term structure of Sharpe ratios.
基金financial support of Gnampa Research Project 2024 (Grant No.PRR-20231026-073916-203)funded in part by an Ermenegildo Zegna Founder's Scholarship (Zullino)。
文摘In the context of risk measures,the capital allocation problem is widely studied in the literature where different approaches have been developed,also in connection with cooperative game theory and systemic risk.Although static capital allocation rules have been extensively studied in the recent years,only few works deal with dynamic capital allocations and its relation with BSDEs.Moreover,all those works only examine the case of an underneath risk measure satisfying cash-additivity and,moreover,a large part of them focuses on the specific case of the gradient allocation where Gateaux differentiability is assumed.The main goal of this paper is,instead,to study general dynamic capital allocations associated to cash-subadditive risk measures,generalizing the approaches already existing in the literature and motivated by the presence of(ambiguity on)interest rates.Starting from an axiomatic approach,we then focus on the case where the underlying risk measures are induced by BSDEs whose drivers depend also on the yvariable.In this setting,we surprisingly find that the corresponding capital allocation rules solve special kinds of Backward Stochastic Volterra Integral Equations(BSVIEs).
