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We prove an anticipative sufficient stochastic minimum principle in a jump process setup with initially enlarged filtrations. We apply the result to several portfolio selection problems like mean and minimal variance hedging under enlarged filtrations. We also investigate utility maximizing portfolio selection under future information. Contrarily to classical optimization methods like dynamic programing, our stochastic minimum principle likewise applies to non-Markovian setups. On the mathematical side, we are concerned with jump processes, forward and backward stochastic differential equations and forward integrals. [ABSTRACT FROM AUTHOR]

We extend the arithmetic multi-factor electricity spot price model proposed by Benth et al. (Appl Math Finance 14(2):153–169, 2007) by adding stochastic mean-level processes to their model and by taking additional information on the future behavior of these mean-level processes into account. The available anticipative information is modeled by an initially enlarged filtration in our paper. We further derive pricing formulas for electricity forwards under future information and investigate the associated information premium. [ABSTRACT FROM AUTHOR]

This paper quantifies the interplay between the no-arbitrage notion of no unbounded profit with bounded risk (NUPBR) and additional progressive information generated by a random time. This study complements the one of Aksamit et al. (Finance Stoch. 21:1103-1139, 2017) in which the authors have studied similar topics for the model stopped at the random time, while here we deal with the question of what happens after the random time. Given that the existing literature proves that NUPBR is always violated after honest times that avoid stopping times in a continuous filtration, we propose here a new class of honest times for which NUPBR can be preserved for some models. For these honest times, we obtain two principal results. The first result characterizes the pairs of initial market and honest time for which the resulting model preserves NUPBR, while the second result characterizes honest times that do not affect NUPBR of any quasi-left-continuous model (i.e., in which the asset price process has no predictable jump times). Furthermore, we construct explicitly local martingale deflators for a large class of models. [ABSTRACT FROM AUTHOR]

This paper studies the impact, on no-arbitrage conditions, of stopping the price process at an arbitrary random time. As price processes, we consider the class of quasi-left-continuous semimartingales, i.e., semimartingales that do not jump at predictable stopping times. We focus on the condition of no unbounded profit with bounded risk (called NUPBR), also known in the literature as no arbitrage of the first kind. The first principal result describes all the pairs of quasi-left-continuous market models and random times for which the resulting stopped model fulfils NUPBR. Furthermore, for a subclass of quasi-left-continuous local martingales, we construct explicitly martingale deflators, i.e., strictly positive local martingales whose product with the price process stopped at a random time is a local martingale. The second principal result characterises the random times that preserve NUPBR under stopping for any quasi-left-continuous model. The analysis carried out in the paper is based on new stochastic developments in the theory of progressive enlargements of filtrations. [ABSTRACT FROM AUTHOR]