This paper studies the weakly and strictly arbitrage-free security markets. The authors extend the Farkas-Minkowski's Lemma and Stiemke's Lemma from two periods to finite periods and from finite-dimensional (E...This paper studies the weakly and strictly arbitrage-free security markets. The authors extend the Farkas-Minkowski's Lemma and Stiemke's Lemma from two periods to finite periods and from finite-dimensional (Euclidean) space to locally convex topological space and separable Banach space, show weakly and strictly arbitrage-free security pricing theory, then obtain the conditional expectation form of weakly and strictly arbitrage-free security pricing formula.展开更多
To capture the subdiffusive characteristics of financial markets, the subordinated process, directed by the inverse α-stale subordinator Sα （t） for 0 〈 α〈 1, has been employed as the model of asset prices. In t...To capture the subdiffusive characteristics of financial markets, the subordinated process, directed by the inverse α-stale subordinator Sα （t） for 0 〈 α〈 1, has been employed as the model of asset prices. In this article, we introduce a multidimensional subdiffusion model that has a bond and K correlated stocks. The stock price process is a multidimen- sional subdiffusion process directed by the inverse a-stable subordinator. This model describes the period of stagnation for each stock and the behavior of the dependency between multiple stocks. Moreover, we derive the multidimensional fractional backward Kolmogorov equation for the subordinated process using the Laplace transform technique. Finally, using a martingale approach, we prove that the multidimensional subdiffusion model is arbitrage-free, and also gives an arbitrage-free pricing rule for contingent claims associated with the martingale measure.展开更多
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 this paper we extend the reduced-form setting under model uncertainty introduced in[5]to include intensities following an affine process under parameter uncertainty,as defined in[15].This framework allows us to int...In this paper we extend the reduced-form setting under model uncertainty introduced in[5]to include intensities following an affine process under parameter uncertainty,as defined in[15].This framework allows us to introduce a longevity bond under model uncertainty in a way consistent with the classical case under one prior and to compute its valuation numerically.Moreover,we price a contingent claim with the sublinear conditional operator such that the extended market is still arbitrage-free in the sense of“no arbitrage of the first kind”as in[6].展开更多
文摘This paper studies the weakly and strictly arbitrage-free security markets. The authors extend the Farkas-Minkowski's Lemma and Stiemke's Lemma from two periods to finite periods and from finite-dimensional (Euclidean) space to locally convex topological space and separable Banach space, show weakly and strictly arbitrage-free security pricing theory, then obtain the conditional expectation form of weakly and strictly arbitrage-free security pricing formula.
基金Project supported by the National Natural Science Foundation of China(Grant No.11171238)
文摘To capture the subdiffusive characteristics of financial markets, the subordinated process, directed by the inverse α-stale subordinator Sα （t） for 0 〈 α〈 1, has been employed as the model of asset prices. In this article, we introduce a multidimensional subdiffusion model that has a bond and K correlated stocks. The stock price process is a multidimen- sional subdiffusion process directed by the inverse a-stable subordinator. This model describes the period of stagnation for each stock and the behavior of the dependency between multiple stocks. Moreover, we derive the multidimensional fractional backward Kolmogorov equation for the subordinated process using the Laplace transform technique. Finally, using a martingale approach, we prove that the multidimensional subdiffusion model is arbitrage-free, and also gives an arbitrage-free pricing rule for contingent claims associated with the martingale measure.
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.
文摘In this paper we extend the reduced-form setting under model uncertainty introduced in[5]to include intensities following an affine process under parameter uncertainty,as defined in[15].This framework allows us to introduce a longevity bond under model uncertainty in a way consistent with the classical case under one prior and to compute its valuation numerically.Moreover,we price a contingent claim with the sublinear conditional operator such that the extended market is still arbitrage-free in the sense of“no arbitrage of the first kind”as in[6].
