2018/08/28 by Elena Boguslavskaya, Boguslavskaya, Elena, Yuliya Mishura +3
Economics, Econometrics and Finance · Mathematics · #60G15 #60G22 #91B16 #91B25 #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:60G15 #msc:60G22 #msc:91B16 #msc:91B25
paper · pdf · doi:10.48550/arxiv.1808.09821
arXiv admin note: text overlap with arXiv:1512.08788
arxiv created 2018/08/28 · openalex publication_date 2018/08/28 · arxiv updated 2018/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate Wiener-transformable markets, where the driving process is given by an adapted transformation of a Wiener process. This includes processes with long memory, like fractional Brownian motion and related processes, and, in general, Gaussian processes satisfying certain regularity conditions on their covariance functions. Our choice of markets is motivated by the well-known phenomena of the so-called `constant' and `variable depth' memory observed in real world price processes, for which fractional and multifractional models are the most adequate descriptions. Motivated by integral representation results in general Gaussian setting, we study the conditions under which random variables can be represented as pathwise integrals with respect to the driving process. From financial point of view, it means that we give the conditions of replication of contingent claims on such markets. As an application of our results, we consider the utility maximization problem in our specific setting. Note that the markets under consideration can be both arbitrage and arbitrage-free, and moreover, we give the representation results in terms of bounded strategies.