The insider trading problem in a jump-binomial model

We study insider trading in a jump-binomial model of the financial market that is based on a marked binomial process and that serves as a suitable alternative to some classical trinomial models. Our investigations focus on the two main questions: measuring the advantage of the insider’s additional information and stating a closed form for her hedging strategy. Our approach is based on the results of enlargement of filtration in a discrete-time setting stated by Blanchet-Scalliet and Jeanblanc (in: From probability to finance, Springer, Berlin, 2020) and on a stochastic analysis for marked binomial processes developed in the companion paper (Halconruy in Electron J Probab 27:1–39, 2022). Our work provides in a discrete-time and an incomplete market setting the analogues of some results of Amendinger et al. (Stoch Process Appl 89(1):101–116, 2000; Finance Stoch 7(1):29–46, 2003), Imkeller et al. (1998, 2006) and extends in an insider framework some utility maximization results stated in Delbaen and Schachermayer (The mathematics of arbitrage, Springer, Berlin, 2006) and in Runggaldier et al. (in: Seminar on stochastic analysis, random fields and applications III, Springer, Berlin, 2002).