Related papers: Trading under the Proof-of-Stake Protocol -- a Con…
In this paper, optimal consumption and investment decisions are studied for an investor who can invest in a fixed interest rate bank account and a stock whose price is a log normal diffusion. We present the method of the HJB equation in…
Trajectory optimization is a fundamental stochastic optimal control problem. This paper deals with a trajectory optimization approach for dynamical systems subject to measurement noise that can be fitted into linear time-varying stochastic…
Blockchain technology, with implications in the financial domain, offers data in the form of large-scale transaction networks. Analyzing transaction networks facilitates fraud detection, market analysis, and supports government regulation.…
In this paper, we provide a novel dynamic decision method of blockchain selfish mining by applying the sensitivity-based optimization theory. Our aim is to find the optimal dynamic blockchain-pegged policy of the dishonest mining pool. To…
In this work we investigate the optimal proportional reinsurance-investment strategy of an insurance company which wishes to maximize the expected exponential utility of its terminal wealth in a finite time horizon. Our goal is to extend…
Proof-of-Work (PoW) is the most widely adopted incentive model in current blockchain systems, which unfortunately is energy inefficient. Proof-of-Stake (PoS) is then proposed to tackle the energy issue. The rich-get-richer concern of PoS…
We consider an investor who is dynamically informed about the future evolution of one of the independent Brownian motions driving a stock's price fluctuations. With linear temporary price impact the resulting optimal investment problem with…
An optimal control problem is considered for a stochastic differential equation with the cost functional determined by a backward stochastic Volterra integral equation (BSVIE, for short). This kind of cost functional can cover the general…
We investigate the general structure of optimal investment and consumption with small proportional transaction costs. For a safe asset and a risky asset with general continuous dynamics, traded with random and time-varying but small…
All public blockchains are secured by a proof of opportunity cost among block producers. For example, the security offered by proof-of-work (PoW) systems, like Bitcoin, is due to spent computation; it is work precisely because it cannot be…
Blockchain plays a crucial role in ensuring the security and integrity of decentralized systems, with the proof-of-work (PoW) mechanism being fundamental for achieving distributed consensus. As PoW blockchains see broader adoption, an…
To implement a blockchain, we need a blockchain protocol for all the nodes to follow. To design a blockchain protocol, we need a block publisher selection mechanism and a chain selection rule. In Proof-of-Stake (PoS) based blockchain…
We study a mechanism design problem in the blockchain proof-of-stake (PoS) protocol. Our main objective is to extend the transaction fee mechanism (TFM) recently proposed in Chung and Shi (SODA, p.3856-3899, 2023), so as to incorporate a…
In this paper, we review the undercutting attacks in the transaction-fee-based regime of proof-of-work (PoW) blockchains with the longest chain fork-choice rule. Next, we focus on the problem of fluctuations in mining revenue and the mining…
We introduce a price impact model which accounts for finite market depth, tightness and resilience. Its coupled bid- and ask-price dynamics induce convex liquidity costs. We provide existence of an optimal solution to the classical problem…
We introduce and study reward sharing schemes (RSS) that promote the fair formation of {\em stake pools}\ in collaborative projects that involve a large number of stakeholders such as the maintenance of a proof-of-stake (PoS) blockchain.…
Proof of Work (PoW) blockchains burn a lot of energy. Proof-of-work algorithms are expensive by design and often only serve to compute blockchains. In some sense, carbon-based and non-carbon based regional electric power is fungible. So the…
This paper introduces a novel methodology for the pricing and management of share buyback contracts, overcoming the limitations of traditional optimal control methods, which frequently encounter difficulties with high-dimensional state…
Bitcoin uses blockchain technology and proof-of-work (PoW) mechanism where nodes spend computing resources and earn rewards in return for spending these resources. This incentive system has caused power to be significantly biased towards a…
An advantageous feature of piecewise constant policy timestepping for Hamilton-Jacobi-Bellman (HJB) equations is that different linear approximation schemes, and indeed different meshes, can be used for the resulting linear equations for…