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We consider non-concave and non-smooth random utility functions with do- main of definition equal to the non-negative half-line. We use a dynamic pro- gramming framework together with measurable selection arguments to establish both the no-arbitrage condition characterization and the existence of an optimal portfolio in a (generically incomplete) discrete-time financial market model with finite time horizon. In contrast to the existing literature, we propose to consider a probability space which is not necessarily complete.
The no-arbitrage property is widely accepted to be a centerpiece of modern financial mathematics and could be considered to be a financial law applicable to a large class of (idealized) markets. The paper addresses the following basic question: can o
We study an optimal dividend problem for an insurer who simultaneously controls investment weights in a financial market, liability ratio in the insurance business, and dividend payout rate. The insurer seeks an optimal strategy to maximize her expec
We extend the result of our earlier study [Angoshtari, Bayraktar, and Young; Optimal consumption under a habit-formation constraint, available at: arXiv:2012.02277, (2020)] to a market setup that includes a risky asset whose price process is a geomet
We design three continuous--time models in finite horizon of a commodity price, whose dynamics can be affected by the actions of a representative risk--neutral producer and a representative risk--neutral trader. Depending on the model, the producer c
We analyze the martingale selection problem of Rokhlin (2006) in a pointwise (robust) setting. We derive conditions for solvability of this problem and show how it is related to the classical no-arbitrage deliberations. We obtai