SOLVABLE AFFINE TERM STRUCTURE MODELS

An Affine Term Structure Model (ATSM) is said to be solvable if the pricing problem has an explicit solution, i.e., the corresponding Riccati ordinary differential equations have a regular globally integrable flow. We identify the parametric restrictions which are necessary and sufficient for an ATSM with continuous paths, to be solvable in a state space     , where     , the domain of positive factors, has the geometry of a symmetric cone. This class of state spaces includes as special cases those introduced by Duffie and Kan (1996) , and Wishart term structure processes discussed by Gourieroux and Sufana (2003) . For all solvable models we provide the procedure to find the explicit solution of the Riccati ODE.     

深水时域格林函数的实用数值计算

如何精确而又快速地计算时域格林函数及其导数是求解船舶水动力问题的关键。论文基于Bessel函数的性质推导了深水格林函数及其导数所满足的常微分方程,提出了结合求解常微分方程的节点制表、节点间插值的快速计算格林函数的方法。数值计算表明该计算方法克服前人节点制表节点间插值计算方法的缺点,提高了格林函数的计算效率和数值精度。     

Stochastic Jacobian and Riccati ODE in affine term structure models

In affine term structure models (ATSM) the stochastic Jacobian under the forward measure plays a crucial role for pricing, as discussed in Elliott and van der Hoek (Finance Stoch 5:511–525, 2001). Their approach leads to a deterministic integro-differential equation which, apparently, has the advantage of by-passing the solution to the Riccati ODE obtained by the standard Feynman-Kac argument. In the generic multi-dimensional case, we find a procedure to reduce such integro-differential equation to a non linear matrix ODE. We prove that its solution does necessarily require the solution of the vector Riccati ODE. This result is obtained proving an extension of the celebrated Radon Lemma, which allows us to highlight a deep relation between the geometry of the Riccati flow and the stochastic calculus of variations for an ATSM. We are grateful to two anonymous referees for their careful reading of the paper.     

Markov chains under nonlinear expectation

In this paper, we consider continuous‐time Markov chains with a finite state space under nonlinear expectations. We define so‐called Q‐operators as an extension of Q‐matrices or rate matrices to a nonlinear setup, where the nonlinearity is due to model uncertainty. The main result gives a full characterization of convex Q‐operators in terms of a positive maximum principle, a dual representation by means of Q‐matrices, time‐homogeneous Markov chains under convex expectations, and a class of nonlinear ordinary differential equations. This extends a classical characterization of generators of Markov chains to the case of model uncertainty in the generator. We further derive an explicit primal and dual representation of convex semigroups arising from Markov chains under convex expectations via the Fenchel–Legendre transformation of the generator. We illustrate the results with several numerical examples, where we compute price bounds for European contingent claims under model uncertainty in terms of the rate matrix.