-
作者：Crisan, Dan; McMurray, Eamon
作者单位：Imperial College London
摘要：We present two cubature on Wiener space algorithms for the numerical solution of McKean-Vlasov SDEs with smooth scalar interaction. First, we consider a method introduced in [Stochastic Process. Appl. 125 (2015) 2206-2255] under a uniformly elliptic assumption and extend the analysis to a uniform strong Hormander assumption. Then we introduce a new method based on Lagrange polynomial interpolation. The analysis hinges on sharp gradient to time-inhomogeneous parabolic PDEs bounds. These bounds ...
-
作者：Gracar, Peter; Stauffer, Alexandre
作者单位：University of Cologne; University of Bath
摘要：Consider the graph induced by Z(d), equipped with uniformly elliptic random conductances. At time 0, place a Poisson point process of particles on Z(d) and let them perform independent simple random walks. Tessellate the graph into cubes indexed by i is an element of Z(d) and tessellate time into intervals indexed by tau. Given a local event E(i, tau) that depends only on the particles inside the space time region given by the cube i and the time interval tau, we prove the existence of a Lipsc...
-
作者：Atar, Rami; Cohen, Asaf
作者单位：Technion Israel Institute of Technology; University of Haifa
摘要：We study a single-server Markovian queueing model with N customer classes in which priority is given to the shortest queue. Under a critical load condition, we establish the diffusion limit of the nominal workload and queue length processes in the form of a Walsh Brownian motion (WBM) living in the union of the N nonnegative coordinate axes in R-N and a linear transformation thereof. This reveals the following asymptotic behavior. Each time that queues begin to build starting from an empty sys...
-
作者：Nadtochiy, Sergey; Shkolnikov, Mykhaylo
作者单位：Illinois Institute of Technology; Princeton University
摘要：We propose an interacting particle system to model the evolution of a system of banks with mutual exposures. In this model, a bank defaults when its normalized asset value hits a lower threshold, and its default causes instantaneous losses to other banks, possibly triggering a cascade of defaults. The strength of this interaction is determined by the level of the so-called noncore exposure. We show that, when the size of the system becomes large, the cumulative loss process of a bank resulting...
-
作者：Cox, Alexander M. G.; Kinsley, Sam M.
作者单位：University of Bath
摘要：A leveraged exchange traded fund (LETF) is an exchange traded fund that uses financial derivatives to amplify the price changes of a basket of goods. In this paper, we consider the robust hedging of European options on a LETF, finding model-free bounds on the price of these options. To obtain an upper bound, we establish a new optimal solution to the Skorokhod embedding problem (SEP) using methods introduced in Beiglbock- Cox-Huesmann. This stopping time can be represented as the hitting time ...
-
作者：Hefter, Mario; Herzwurm, Andre; Mueller-Gronbach, Thomas
作者单位：Austrian Academy of Sciences; University of Kaiserslautern; University of Passau
摘要：We study pathwise approximation of scalar stochastic differential equations at a single time point or globally in time by means of methods that are based on finitely many observations of the driving Brownian motion. We prove lower error bounds in terms of the average number of evaluations of the driving Brownian motion that hold for every such method under rather mild assumptions on the coefficients of the equation. The underlying simple idea of our analysis is as follows: the lower error boun...
-
作者：Muirhead, S.; Pymar, R.; dos Santos, R. S.
作者单位：University of London; King's College London; University of London; Birkbeck University London; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：The Bouchaud-Anderson model (BAM) is a generalisation of the parabolic Anderson model (PAM) in which the driving simple random walk is replaced by a random walk in an inhomogeneous trapping landscape; the BAM reduces to the PAM in the case of constant traps. In this paper, we study the BAM with double-exponential potential. We prove the complete localisation of the model whenever the distribution of the traps is unbounded. This may be contrasted with the case of constant traps (i.e., the PAM),...
-
作者：Bartl, Daniel
作者单位：University of Konstanz
摘要：We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of nondominated probabilistic models of her endowment by dynamically investing in a financial market, and statically in available options. We show that, for any measurable random endowment (regardless of whether the problem is finite or not) an optimal strategy exists, a dual representation in terms of (calibrated) martinga...
-
作者：Benaim, Michel; Strickler, Edouard
作者单位：University of Neuchatel
摘要：Let E be a finite set, {F-i}(i is an element of E) a family of vector fields on R-d leaving positively invariant a compact set M and having a common zero p is an element of M. We consider a piecewise deterministic Markov process (X, I) on M x E defined by (X)over dot(t)=F(I)t(X-t) where I is a jump process controlled by X: Pr(It+s = j vertical bar(X-u ,I-u)(u <= t)) = a(ij)(X-t)(s) + o(s) for i not equal j on {I-t=i}. We show that the behaviour of (X, I) is mainly determined by the behaviour o...
-
作者：Peskir, Goran
作者单位：University of Manchester
摘要：We first show that a smooth fit between the value function and the gain function at the optimal stopping boundary for a two-dimensional diffusion process implies the absence of boundary's discontinuities of the first kind (the right-hand and left-hand limits exist but differ). We then show that the smooth fit itself is satisfied over the flat portion of the optimal stopping boundary arising from any of its hypothesised jumps. Combining the two facts we obtain that the optimal stopping boundary...
