Blockchains are characterized by algorithms for synchronizing data between network nodes (consensus), methods of data storage, and the programs executed on them (smart contracts). The talk will examine each of these aspects using selected tasks as examples: fault-tolerant random number generation, trees for provable responses to user queries, and risk of a platform for cryptocurrency-backed lending.

References:

[1] Krasnoselskii, M., Melnikov, G., & Yanovich, Y. (2020). No-dealer: Byzantine fault-tolerant random number generator. In IEEE INFOCOM 2020-IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS).

[2] Krasnoselskii, M., Melnikov, G., & Yanovich, Y. (2021). DisCO: Peer-to-Peer Random Number Generator in Partial Synchronous Systems. In 2021 3rd Conference on Blockchain Research & Applications for Innovative Networks and Services (BRAINS).
[3] Chaleenutthawut, Y., Davydov, V., Evdokimov, M., Kasemsuk, S., Kruglik, S., Melnikov, G., & Yanovich, Y. (2024). Loan Portfolio Dataset From MakerDAO Blockchain Project. IEEE Access.

Aiming to analyze the impact of environmental transition on the value of assets and on asset stranding, we study optimal stopping and divestment timing decisions for an economic agent whose future revenues depend on the realization of a scenario from a given set of possible futures. Since the future scenario is unknown and the probabilities of individual prospective scenarios are ambiguous, we adopt the smooth model of decision making under ambiguity aversion of Klibanoff et al (2005), framing the optimal divestment decision as an optimal stopping problem with learning under ambiguity aversion. We then prove a minimax result reducing this problem to a series of standard optimal stopping problems with learning. The theory is illustrated with two examples: the problem of optimally selling a stock with ambigous drift, and the problem of optimal divestment from a coal-fired power plant under transition scenario ambiguity.

In this paper we study optimal investment when the investor can peek some time units into the future, but cannot fully take advantage of this knowledge because of quadratic transaction costs. In the Bachelier setting with exponential utility, we give an explicit solution to this control problem with intrinsically infinite-dimensional memory. This is made possible by solving the dual problem where we make use of the theory of Gaussian Volterra integral equations. Joint work with Peter Bank and Miklos Rasonyi.

In this paper, we provide a general approach to reformulating any continuous-time stochastic Stackelberg differential game under closed-loop strategies as a single-level optimisation problem with target constraints. More precisely, we consider a Stackelberg game in which the leader and the follower can both control the drift and the volatility of a stochastic output process, in order to maximise their respective expected utility. The aim is to characterise the Stackelberg equilibrium when the players adopt "closed-loop strategies", i.e. their decisions are based solely on the historical information of the output process, excluding especially any direct dependence on the underlying driving noise, often unobservable in real-world applications. We first show that, by considering the-second-order-backward stochastic differential equation associated with the continuation utility of the follower as a controlled state variable for the leader, the latter’s unconventional optimisation problem can be reformulated as a more standard stochastic control problem with stochastic target constraints. Thereafter, adapting the methodology developed by Soner and Touzi or Bouchard, Élie, and Imbert, the optimal strategies, as well as the corresponding value of the Stackelberg equilibrium, can be characterised through the solution of a well-specified system of Hamilton-Jacobi-Bellman equations. For a more comprehensive insight, we illustrate our approach through a simple example, facilitating both theoretical and numerical detailed comparisons with the solutions under different information structures studied in the literature. This is a joint work with Camilo Hernández, Nicolás Hernández Santibáñez, and Emma Hubert.