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Decentralized Finance (DeFi) is a new paradigm in the creation, distribution, and utilization of financial services via the integration of blockchain technology. Our research conducts a comprehensive introduction and meticulous…
Decentralized Finance (DeFi) is a new financial industry built on blockchain technologies. Decentralized financial services have consequently increased the ability to lend, borrow, and invest in decentralized investment vehicles, allowing…
In this paper we derive a Bismut-Elworthy-Li type formula with respect to strong solutions to singular stochastic differential equations (SDE's) with additive noise given by a multi-dimensional fractional Brownian motion with Hurst…
Decentralised Finance (DeFi) applications constitute an entire financial ecosystem deployed on blockchains. Such applications are based on complex protocols and incentive mechanisms whose financial safety is hard to determine. Besides,…
Financial options are fundamental to traditional markets, enabling strategies ranging from hedging to speculating. Yet, while the Automated Market Maker paradigm has revolutionized decentralized spot markets, no equivalent standard has…
We develop a mathematical framework to optimize leveraged staking ("loopy") strategies in Decentralized Finance (DeFi), in which a staked asset is supplied as collateral, the underlying is borrowed and re-staked, and the loop can be…
We compute the rate of decay of the persistence probabilities of spherical fractional Brownian motion, which was defined by L\'evy (1965) and Istas (2005). The rate resembles the Euclidean case treated in Molchan (1999). As a by-product we…
We study the problem of optimally hedging the price exposure of liquidity positions in constant-product automated market makers (AMMs) when the hedge is funded by collateralized borrowing. A liquidity provider (LP) who borrows tokens to…
Motivated by the interplay between structural and reduced form credit models, we propose to model the firm value process as a time-changed Brownian motion that may include jumps and stochastic volatility effects, and to study the first…
This paper develops a two-dimensional structural framework for valuing credit default swaps and corporate bonds in the presence of default contagion. Modelling the values of related firms as correlated geometric Brownian motions with…
We introduce a canonical way of performing the joint lift of a Brownian motion $W$ and a low-regularity adapted stochastic rough path $\mathbf{X}$, extending [Diehl, Oberhauser and Riedel (2015). A L\'evy area between Brownian motion and…
Decentralised exchanges (DEXs) have transformed trading by enabling trustless, permissionless transactions, yet they face significant challenges such as impermanent loss and slippage, which undermine profitability for liquidity providers…
We consider two insurance companies with endowment processes given by Brownian motions with drift. The firms can collaborate by transfer payments in order to maximize the probability that none of them goes bankrupt. We show that pushing…
The aim of this paper is to present the new results concerning some functionals of Brownian motion with drift and present their applications in financial mathematics. We find a probabilistic representation of the Laplace transform of…
Decentralized Finance (DeFi) refers to financial services that are not necessarily related to crypto-currencies. By employing blockchain for security and integrity, DeFi creates new possibilities that attract retail and institution users,…
Developing devices using disordered organic semiconductors requires accurate and practical models of charge transport. In these materials, charge transport occurs through partially delocalised states in an intermediate regime between…
This paper presents a new model for pricing financial derivatives subject to collateralization. It allows for collateral arrangements adhering to bankruptcy laws. As such, the model can back out the market price of a collateralized…
We discuss a general dynamic replication approach to counterparty credit risk modeling. This leads to a fundamental jump-process backward stochastic differential equation (BSDE) for the credit risk adjusted portfolio value. We then reduce…
Correlations among stock returns during volatile markets differ substantially compared to those from quieter markets. During times of financial crisis, it has been observed that traditional dependency in global markets breaks down. However,…
Stablecoins are one of the most widely capitalized type of cryptocurrency. However, their risks vary significantly according to their design and are often poorly understood. We seek to provide a sound foundation for stablecoin theory, with…