arXiv subjects

Agostino Capponi

Publications and source records attributed to Agostino Capponi.

At least 37 records · Page 2Linked to original sources

arXiv2024

The Paradox Of Just-in-Time Liquidity in Decentralized Exchanges: More Providers Can Sometimes Mean Less Liquidity

We study Just-in-time (JIT) liquidity provision in blockchain-based decentralized exchanges. A JIT liquidity provider (LP) monitors pending swap orders in public mempools of blockchains to sandwich orders of their choice with liquidity, depositing right before and withdrawing right after the order. Our game-theoretic model with asymmetrically informed agents reveals that a JIT LP's presence does not always enhance liquidity pool depth, as one might expect. While passive LPs face adverse selection by informed arbitrageurs, a JIT LP's ability to detect pending orders for toxic order flow prior to liquidity provision lets them avoid being adversely selected. JIT LPs thus only provide liquidity to uninformed orders and crowd out passive LPs when order volume is not sufficiently elastic to pool depth, possibly reducing overall market liquidity. We show that using a two-tiered fee structure which transfers a part of a JIT LP's fee revenue to passive LPs or allowing for JIT LPs to compete à la Cournot are potential solutions to mitigate the negative effects of JIT liquidity.

q-fin.GN↗

arXiv2023

Exact Error in Matrix Completion: Approximately Low-Rank Structures and Missing Blocks

We study the completion of approximately low rank matrices with entries missing not at random (MNAR). In the context of typical large-dimensional statistical settings, we establish a framework for the performance analysis of the nuclear norm minimization ($\ell_1^*$) algorithm. Our framework produces \emph{exact} estimates of the worst-case residual root mean squared error and the associated phase transitions (PT), with both exhibiting remarkably simple characterizations. Our results enable to {\it precisely} quantify the impact of key system parameters, including data heterogeneity, size of the missing block, and deviation from ideal low rankness, on the accuracy of $\ell_1^*$-based matrix completion. To validate our theoretical worst-case RMSE estimates, we conduct numerical simulations, demonstrating close agreement with their numerical counterparts.

cs.IT↗

arXiv2023

Decentralized Finance: Protocols, Risks, and Governance

Financial markets are undergoing an unprecedented transformation. Technological advances have brought major improvements to the operations of financial services. While these advances promote improved accessibility and convenience, traditional finance shortcomings like lack of transparency and moral hazard frictions continue to plague centralized platforms, imposing societal costs. In this paper, we argue how these shortcomings and frictions are being mitigated by the decentralized finance (DeFi) ecosystem. We delve into the workings of smart contracts, the backbone of DeFi transactions, with an emphasis on those underpinning token exchange and lending services. We highlight the pros and cons of the novel form of decentralized governance introduced via the ownership of governance tokens. Despite its potential, the current DeFi infrastructure introduces operational risks to users, which we segment into five primary categories: consensus mechanisms, protocol, oracle, frontrunning, and systemic risks. We conclude by emphasizing the need for future research to focus on the scalability of existing blockchains, the improved design and interoperability of DeFi protocols, and the rigorous auditing of smart contracts.

q-fin.TR↗

arXiv2023

Causal Inference (C-inf) -- closed form worst case typical phase transitions

In this paper we establish a mathematically rigorous connection between Causal inference (C-inf) and the low-rank recovery (LRR). Using Random Duality Theory (RDT) concepts developed in [46,48,50] and novel mathematical strategies related to free probability theory, we obtain the exact explicit typical (and achievable) worst case phase transitions (PT). These PT precisely separate scenarios where causal inference via LRR is possible from those where it is not. We supplement our mathematical analysis with numerical experiments that confirm the theoretical predictions of PT phenomena, and further show that the two closely match for fairly small sample sizes. We obtain simple closed form representations for the resulting PTs, which highlight direct relations between the low rankness of the target C-inf matrix and the time of the treatment. Hence, our results can be used to determine the range of C-inf's typical applicability.

stat.ML↗

arXiv2023

Causal Inference (C-inf) -- asymmetric scenario of typical phase transitions

In this paper, we revisit and further explore a mathematically rigorous connection between Causal inference (C-inf) and the Low-rank recovery (LRR) established in [10]. Leveraging the Random duality - Free probability theory (RDT-FPT) connection, we obtain the exact explicit typical C-inf asymmetric phase transitions (PT). We uncover a doubling low-rankness phenomenon, which means that exactly two times larger low rankness is allowed in asymmetric scenarios compared to the symmetric worst case ones considered in [10]. Consequently, the final PT mathematical expressions are as elegant as those obtained in [10], and highlight direct relations between the targeted C-inf matrix low rankness and the time of treatment. Our results have strong implications for applications, where C-inf matrices are not necessarily symmetric.

stat.ML↗

arXiv2022

Large Sample Mean-Field Stochastic Optimization

We study a class of sampled stochastic optimization problems, where the underlying state process has diffusive dynamics of the mean-field type. We establish the existence of optimal relaxed controls when the sample set has finite size. The core of our paper is to prove, via $Γ$-convergence, that the minimizer of the finite sample relaxed problem converges to that of the limiting optimization problem. We connect the limit of the sampled objective functional to the unique solution, in the trajectory sense, of a nonlinear Fokker-Planck-Kolmogorov (FPK) equation in a random environment. We highlight the connection between the minimizers of our optimization problems and the optimal training weights of a deep residual neural network.

math.OC↗

arXiv2022

The Evolution of Blockchain: from Lit to Dark

Transactions submitted through the blockchain peer-to-peer (P2P) network may leak out exploitable information. We study the economic incentives behind the adoption of blockchain dark venues, where users' transactions are observable only by miners on these venues. We show that miners may not fully adopt dark venues to preserve rents extracted from arbitrageurs, hence creating execution risk for users. The dark venue neither eliminates frontrunning risk nor reduces transaction costs. It strictly increases the payoff of miners, weakly increases the payoff of users, and weakly reduces arbitrageurs' profits. We provide empirical support for our main implications, and show that they are economically significant. A 1% increase in the probability of being frontrun raises users' adoption rate of the dark venue by 0.6%. Arbitrageurs' cost-to-revenue ratio increases by a third with a dark venue.

q-fin.GN↗

arXiv2022

Power Forward Performance in Semimartingale Markets with Stochastic Integrated Factors

We study the forward investment performance process (FIPP) in an incomplete semimartingale market model with closed and convex portfolio constraints, when the investor's risk preferences are of the power form. We provide necessary and sufficient conditions for the construction of such a performance process, and show that it can be recovered as the unique solution of an infinite horizon quadratic backward stochastic differential equation (BSDE) with a nonmonotone driver. In an integrated stochastic factor model, we relate the factor representation of the BSDE solution to the smooth solution of an ill-posed partial integro-differential Hamilton-Jacobi-Bellman (HJB) equation. We provide an explicit construction of the BSDE solution for the class of time-monotone FIPPs, generalizing existing results from Brownian to semimartingale market models.

math.PR↗

arXiv2022

Power Forward Performance in Semimartingale Markets with Stochastic Integrated Factors

We study the forward investment performance process (FIPP) in an incomplete semimartingale market model with closed and convex portfolio constraints, when the investor's risk preferences are of the power form. We provide necessary and sufficient conditions for the existence of such FIPP. In a semimartingale factor model, we show that the FIPP can be recovered as a triplet of processes which admit an integral representation with respect to semimartingales. Using an integrated stochastic factor model, we relate the factor representation of the triplet of processes to the smooth solution of an ill-posed partial integro-differential Hamilton-Jacobi-Bellman (HJB) equation. We develop explicit constructions for the class of time-monotone FIPPs, generalizing existing results from Brownian to semimartingale market models.

q-fin.PM↗

arXiv2021

The Adoption of Blockchain-based Decentralized Exchanges

We investigate the market microstructure of Automated Market Makers (AMMs), the most prominent type of blockchain-based decentralized exchanges. We show that the order execution mechanism yields token value loss for liquidity providers if token exchange rates are volatile. AMMs are adopted only if their token pairs are of high personal use for investors, or the token price movements of the pair are highly correlated. A pricing curve with higher curvature reduces the arbitrage problem but also investors' surplus. Pooling multiple tokens exacerbates the arbitrage problem. We provide statistical support for our main model implications using transaction-level data of AMMs.

q-fin.TR↗

arXiv2021

Proof-of-Work Cryptocurrencies: Does Mining Technology Undermine Decentralization?

Does the proof-of-work protocol serve its intended purpose of supporting decentralized cryptocurrency mining? To address this question, we develop a game-theoretical model where miners first invest in hardware to improve the efficiency of their operations, and then compete for mining rewards in a rent-seeking game. We argue that because of capacity constraints faced by miners, centralization in mining is lower than indicated by both public discourse and recent academic work. We show that advancements in hardware efficiency do not necessarily lead to larger miners increasing their advantage, but rather allow smaller miners to expand and new miners to enter the competition. Our calibrated model illustrates that hardware efficiency has a small impact on the cost of attacking a network, while the mining reward has a significant impact. This highlights the vulnerability of smaller and emerging cryptocurrencies, as well as of established cryptocurrencies transitioning to a fee-based mining reward scheme.

q-fin.TR↗

arXiv2021

Market Efficient Portfolios in a Systemic Economy

We study the ex-ante minimization of market inefficiency, defined in terms of minimum deviation of market prices from fundamental values, from a centralized planner's perspective. Prices are pressured from exogenous trading actions of leverage targeting banks, which rebalance their portfolios in response to asset shocks. We characterize market inefficiency in terms of two key drivers, the banks' systemic significance and the statistical moments of asset shocks, and develop an explicit expression for the matrix of asset holdings which minimizes such inefficiency. Our analysis shows that to reduce inefficiencies, portfolio holdings should deviate more from a full diversification strategy if there is little heterogeneity in banks' systemic significance.

q-fin.RM↗

arXiv2021

Market Making with Stochastic Liquidity Demand: Simultaneous Order Arrival and Price Change Forecasts

We provide an explicit characterization of the optimal market making strategy in a discrete-time Limit Order Book (LOB). In our model, the number of filled orders during each period depends linearly on the distance between the fundamental price and the market maker's limit order quotes, with random slope and intercept coefficients. The high-frequency market maker (HFM) incurs an end-of-the-day liquidation cost resulting from linear price impact. The optimal placement strategy incorporates in a novel and parsimonious way forecasts about future changes in the asset's fundamental price. We show that the randomness in the demand slope reduces the inventory management motive, and that a positive correlation between demand slope and investors' reservation prices leads to wider spreads. Our analysis reveals that the simultaneous arrival of buy and sell market orders (i) reduces the shadow cost of inventory, (ii) leads the HFM to reduce price pressures to execute larger flows, and (iii) introduces patterns of nonlinearity in the intraday dynamics of bid and ask spreads. Our empirical study shows that the market making strategy outperforms those which ignores randomness in demand, simultaneous arrival of buy and sell market orders, and local drift in the fundamental price.

q-fin.TR↗

arXiv2020

Personalized Robo-Advising: Enhancing Investment through Client Interaction

Automated investment managers, or robo-advisors, have emerged as an alternative to traditional financial advisors. The viability of robo-advisors crucially depends on their ability to offer personalized financial advice. We introduce a novel framework, in which a robo-advisor interacts with a client to solve an adaptive mean-variance portfolio optimization problem. The risk-return tradeoff adapts to the client's risk profile, which depends on idiosyncratic characteristics, market returns, and economic conditions. We show that the optimal investment strategy includes both myopic and intertemporal hedging terms which are impacted by the dynamics of the client's risk profile. We characterize the optimal portfolio personalization via a tradeoff faced by the robo-advisor between receiving client information in a timely manner and mitigating behavioral biases in the risk profile communicated by the client. We argue that the optimal portfolio's Sharpe ratio and return distribution improve if the robo-advisor counters the client's tendency to reduce market exposure during economic contractions when the market risk-return tradeoff is more favorable.

q-fin.PM↗

arXiv2020

Risk Preferences and Efficiency of Household Portfolios

We propose a novel approach to infer investors' risk preferences from their portfolio choices, and then use the implied risk preferences to measure the efficiency of investment portfolios. We analyze a dataset spanning a period of six years, consisting of end of month stock trading records, along with investors' demographic information and self-assessed financial knowledge. Unlike estimates of risk aversion based on the share of risky assets, our statistical analysis suggests that the implied risk aversion coefficient of an investor increases with her wealth and financial literacy. Portfolio diversification, Sharpe ratio, and expected portfolio returns correlate positively with the efficiency of the portfolio, whereas a higher standard deviation reduces the efficiency of the portfolio. We find that affluent and financially educated investors as well as those holding retirement related accounts hold more efficient portfolios.

q-fin.PM↗

arXiv2020

Robust XVA

We introduce an arbitrage-free framework for robust valuation adjustments. An investor trades a credit default swap portfolio with a risky counterparty, and hedges credit risk by taking a position in defaultable bonds. The investor does not know the return rate of her counterparty's bond, but is confident that it lies within an uncertainty interval. We derive both upper and lower bounds for the XVA process of the portfolio, and show that these bounds may be recovered as solutions of nonlinear ordinary differential equations. The presence of collateralization and closeout payoffs leads to important differences with respect to classical credit risk valuation. The value of the super-replicating portfolio cannot be directly obtained by plugging one of the extremes of the uncertainty interval in the valuation equation, but rather depends on the relation between the XVA replicating portfolio and the close-out value throughout the life of the transaction. Our comparative statics analysis indicates that credit contagion has a nonlinear effect on the replication strategies and on the XVA.

q-fin.PR↗

arXiv2019

Robo-advising: Learning Investors' Risk Preferences via Portfolio Choices

We introduce a reinforcement learning framework for retail robo-advising. The robo-advisor does not know the investor's risk preference, but learns it over time by observing her portfolio choices in different market environments. We develop an exploration-exploitation algorithm which trades off costly solicitations of portfolio choices by the investor with autonomous trading decisions based on stale estimates of investor's risk aversion. We show that the algorithm's value function converges to the optimal value function of an omniscient robo-advisor over a number of periods that is polynomial in the state and action space. By correcting for the investor's mistakes, the robo-advisor may outperform a stand-alone investor, regardless of the investor's opportunity cost for making portfolio decisions.

q-fin.PM↗

arXiv2018

Portfolio Choice with Market-Credit Risk Dependencies

We study an optimal investment/consumption problem in a model capturing market and credit risk dependencies. Stochastic factors drive both the default intensity and the volatility of the stocks in the portfolio. We use the martingale approach and analyze the recursive system of nonlinear Hamilton-Jacobi-Bellman equations associated with the dual problem. We transform such a system into an equivalent system of semi-linear PDEs, for which we establish existence and uniqueness of a bounded global classical solution. We obtain explicit representations for the optimal strategy, consumption path and wealth process, in terms of the solution to the recursive system of semi-linear PDEs. We numerically analyze the sensitivity of the optimal investment strategies to risk aversion, default risk and volatility.

q-fin.MF↗