1st Mini-Workshop on Mathematical Finance at KHU

Abstact:  This paper studies what individual preference factors cause YOLO-like behaviors of consumption and labor-leisure choices in a rational economic agent's framework. We examine whether these YOLO life patterns are sustainable in the long run. To do so, we set up a dynamic optimal consumption, labor-leisure choice, and risky investment decision problem of an agent with recursive preference. The flexible labor-leisure choice setup leads to a non-linear free-boundary value problem. We suggest a novel method to derive optimal policies in closed form by which we categorize types of agents, and then investigate their long-run sustainability.

Abstact: We propose a mean field game model to study the question of how centralization of reward and computational power occur in Bitcoin-like cryptocurrencies. Miners compete against each other for mining rewards by increasing their computational power. This leads to a novel mean field game of jump intensity control, which we solve explicitly for miners maximizing exponential utility, and handle numerically in the case of miners with power utilities. We show that the heterogeneity of their initial wealth distribution leads to greater imbalance of the reward distribution, and increased wealth heterogeneity over time, or a "rich get richer" effect. This concentration phenomenon is aggravated by a higher bitcoin mining reward, and reduced by competition. Additionally, an advantaged miner with cost advantages such as access to cheaper electricity, contributes a significant amount of computational power in equilibrium, unaffected by competition from less efficient miners. Hence, cost efficiency can also result in the type of centralization seen among miners of cryptocurrencies.

Abstract: We explore an optimal token holding and staking problem for cryptocurrency investors. Our investigation revolves around understanding the tradeoff between staking rewards/utility and the consequent illiquidity that emerges as a result of investor heterogeneity and the distinct structure of blockchain platforms or Decentralized Autonomous Organizations (DAOs). We present comprehensive analytic solutions, which enable us to examine the novel facets and implications stemming from the staking mechanism for trading and staking policies and the dynamics of risk-taking behaviors. These insights extend beyond token investments devoid of staking rewards and conventional investment avenues, such as stocks and commodities.

Abstract: In this talk we provide a sensitivity analysis for robust optimization problems, where model ambiguity is captured by a closed ball (with respect to some suitable norms) around each semimartingale differential characteristic of a postulated reference Itô-semimartingale. Assuming a decision maker seeks to derive a robust control such that its stochastic integral optimizes her minimax value function, the first-order correction, which is defined as the first-order derivative of the minimax value function with respect to the radius of the ball at 0, is obtained. In particular, the correction is characterized in terms of the optimizer of the value function under the postulated reference semimartingale without model ambiguity and the function’s gradient at the optimum. The approach relies on dual norm representations and the tools of back- ward stochastic differential equations. In the context of finance and economics, some possible applications and extensions are discussed within the proposed results. This talk is based on a joint work with Daniel Bartl and Ariel Neufeld.