February 2024
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43 Reads
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6 Citations
Journal of Econometrics
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Publications (119)
June 2023
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18 Reads
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32 Citations
Management Science
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. This paper was accepted by Kay Giesecke, finance. Funding: A. M. Reppen is partly supported by the Swiss National Science Foundation [Grant SNF 181815]. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2023.4798 .
May 2023
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12 Reads
Applied Mathematical Finance
Accelerated share repurchases (ASRs) are a type of stock buyback wherein the repurchasing firm contracts a financial intermediary to acquire the shares on its behalf. The intermediary purchases the shares from the open market and is compensated by the firm according to the average of the stock price over the repurchasing interval, whose end can be chosen by the intermediary. Hence, the intermediary needs to decide both how to minimize the cost of acquiring the shares, and when to exercise its contract to maximize its payment. Studies of ASRs typically assume a constant volatility, but the longer time horizon of ASRs, on the order of months, indicates that the variation of the volatility should be considered. We analyze the optimal strategy of the intermediary within the continuous-time framework of the Heston model for the evolution of the stock price and volatility, which is described by a free-boundary problem which we derive here. To solve this system numerically, we make use of deep learning. Through simulations, we find that the intermediary can acquire shares at lower cost and lower risk if it takes into account the stochasticity of the volatility.
May 2023
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22 Reads
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2 Citations
Risk and Decision Analysis
We study paycheck optimization, which examines how to allocate income in order to achieve several competing financial goals. For paycheck optimization, a quantitative methodology is missing, due to a lack of a suitable problem formulation. To deal with this issue, we formulate the problem as a utility maximization problem. The proposed formulation is able to (i) unify different financial goals; (ii) incorporate user preferences regarding the goals; (iii) handle stochastic interest rates. The proposed formulation also facilitates an end-to-end reinforcement learning solution, which is implemented on a variety of problem settings.
January 2023
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30 Reads
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10 Citations
Journal of Differential Equations
We establish the existence and uniqueness of a solution to the master equation for a mean field game of controls with absorption. The mean field game arises as a continuum limit of a dynamic game of exhaustible resources modeling Cournot competition between producers. The proof relies on an analysis of a forward-backward system of nonlocal Hamilton-Jacobi/Fokker-Planck equations with Dirichlet boundary conditions. In particular, we establish new a priori estimates to prove that solutions are differentiable with respect to the initial measure.
November 2022
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28 Reads
We formulate a model of the banking system in which banks control both their supply of liquidity, through cash holdings, and their exposures to risky interbank loans. The value of interbank loans jumps when banks suffer liquidity shortages, which can be caused by the arrival of large enough liquidity shocks. In two distinct settings, we compute the unique optimal allocations of capital. In the first, banks seek only to maximize their own utility -- in a decentralized manner. Second, a central planner aims to maximize the sum of all banks' utilities. Both of the resulting financial networks exhibit a `core-periphery' structure. However, the optimal allocations differ -- decentralized banks are more susceptible to liquidity shortages, while the planner ensures that banks with more debt hold greater liquidity. We characterize the behavior of the planner's optimal allocation as the size of the system grows. Surprisingly, the `price of anarchy' is of constant order. Finally, we derive capitalization requirements that cause the decentralized system to achieve the planner's level of risk. In doing so, we find that systemically important banks must face the greatest losses when they suffer liquidity crises -- ensuring that they are incentivized to avoid such crises.
October 2022
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17 Reads
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6 Citations
SIAM Journal on Control and Optimization
September 2022
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11 Reads
SIAM Journal on Financial Mathematics
March 2022
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16 Reads
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1 Citation
SIAM Journal on Financial Mathematics
January 2022
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3 Reads
SSRN Electronic Journal
Citations (69)
... volatility (Pastor & Veronesi, 2012;Barroso & Detzel, 2021) or model the disconnect directly (Aït-Sahalia et al., 2024). ...
- Citing Article
February 2024
Journal of Econometrics
... That said, these methods do not, by themselves, attempt to limit the size of state spaces and can generate large small sample bias in the presence of complex ones. (iii) The estimation problem can also be seen as a maximal entropy inverse reinforcement learning (IRL) prob-lem [Ermon et al., 2015], which facilitates machine learning solutions [Geng et al., 2020, Yoganarasimhan, 2018. Although machine learning methods accommodate large state spaces using powerful function approximators, these approximators require large datasets and underperform in small samples. ...
- Citing Conference Paper
- Full-text available
June 2020
... Benazzoli et al. (2017Benazzoli et al. ( , 2020 gave a detailed analysis of the MFG with controlled jumps. Li et al. (2023) presented a comprehensive framework of using MFG to investigate and solve the competitive multi-player games involving jump processes in cryptocurrency mining, but without including a diffusion term in the stochastic process. However, these studies have not incorporated the specific MFG model of green and brown companies, nor have they integrated green insurance with green economy or considered the green investments of insurers. ...
Reference:
A mean field game model of green economy
- Citing Article
June 2023
Management Science
... Besides, our proposed insights evaluation methods may have broader impact on other real-world use-cases such as in healthcare, finance, bank sales etc. For example, quantifying the estimated contributions of biological risk factors on healthcare costs [42] or examining the effectiveness of a predicted business decision from an AI agent on the company's income/loss [4]. ...
- Citing Article
May 2023
Risk and Decision Analysis
... We show that mean field games such as the one considered in [CS17] satisfy the (Σ) condition but are not Lasry-Lions monotone. This observation leads us to believe that recent results on Cournot competition [JGIN21,GS23] could be improved by dispensing with the "smallness condition" used to prove uniqueness. Nevertheless, in this paper we deal only with first-order models without boundary conditions or state constraints, thus avoiding the heavy technicalities and focusing solely on the issue of monotonicity. ...
- Citing Article
January 2023
Journal of Differential Equations
... Their analysis is based on a sophisticated, yet abstract fixed point argument which makes it difficult to solve MFGs in closed form. A very different approach that applies to a different class of deterministic MFGs has recently been taken by Graewe et al. [26]. They considered a deterministic linear-quadratic MFG of control in which players extract an exhaustible resource and drop out of the game as soon as their resources hit zero. ...
- Citing Article
October 2022
SIAM Journal on Control and Optimization
... Moreover, particularly since the financial crisis, there seems to be a disconnect between the EPU and realized volatility. Such a disconnect of uncertainty and volatility was recently studied in Aït-Sahalia et al. (2021) for equity markets to explain the challenges faced by previous empirical studies trying to establish a risk-return trade-off using volatility alone as a measure of risk. While in our paper, we do not delve deeper into this disconnect for interest rate dynamics, Panel B of Figure 1 indicates that there is a subtle difference between the EPU and interest rate volatility. ...
- Citing Article
September 2021
Finance and Economics Discussion Series
... In his review of the 2007 Stern Review of the Economics of Climate Change (Stern, 2007) [186], Weitzman (2007) [195] suggests that the standard risk analysis method of truncating tails of the distribution is incompatible with the thick tail of negative potential climate outcomes. 6 This was also an explicit concern of Mastrandrea et al. (2011) [144], who developed the guidance on how the authors of the Intergovernmental Panel on Climate Change Hoffman, and Phan (2019) [60], and Desmet et al. (2021) [74]. 6 Truncation is most justified when the economic salience of an outcome drops faster than the probability of that outcome-the opposite of the fat-tailed case of climate change. ...
- Citing Article
January 2021
SSRN Electronic Journal
... For example, some early studies on the predictability of stock returns using the stochastic factor can be found in Fama and Schwert (1977), Ferson and Harvey (1993), Brennan et al. (1997), Brennan (1998), Campbell and Viceira (1999), Wachter (2002) among others. The optimal investment under the stochastic volatility and unhedgeable risk or the combination of the stochastic returns and stochastic volatility was investigated in French et al. (1987), Kim and Omberg (1996), Scruggs (1998), Fouque et al. (2000), Zariphopoulou (2001), Pham (2002), Fleming and Hernández-Hernández (2003), Chacko and Viceira (2005), Kraft (2005), Castaneda-Leyva and Hernández-Hernández (2005), Liu (2007), Fouque et al. (2013), Hata et al. (2018), Avanesyan et al. (2020), to name a few. ...
- Citing Article
- Publisher preview available
October 2020
Finance and Stochastics
... This class of models dates back to Tirole (1988), Segerstrom, Anant and Dinopoulos (1990), Grossman and Helpman (1991), Aghion and Howitt (1992) and Budd, Harris and Vickers (1993), 1 See Aghion, Antonin and Bunel (2021) and Akcigit and Ates (2021) for extensive reviews. and recent applications include Aghion et al. (2001), Aghion et al. (2005, Ludkovski and Sircar (2016), Liu, Mian and Su (2019) and Akcigit and Ates (2021). Our model features one novelty: we model the negative pro t shock and explore its impact on the optimal behaviors of rms with heterogeneous costs and technology gaps in the long run. ...
- Citing Article
January 2015
SSRN Electronic Journal