Motivated by recent applications of sequential decision making in matching markets, in this paper we attempt at formulating and abstracting market designs for P2P lending. We describe a paradigm to set the stage for how peer to peer investments can be conceived from a matching market perspective, especially when both borrower and lender preferences are respected. We model these specialized markets as an optimization problem and consider different utilities for agents on both sides of the market while also understanding the impact of equitable allocations to borrowers. We devise a technique based on sequential decision making that allow the lenders to adjust their choices based on the dynamics of uncertainty from competition over time and that also impacts the rewards in return for their investments. Using simulated experiments we show the dynamics of the regret based on the optimal borrower-lender matching and find that the lender regret depends on the initial preferences set by the lenders which could affect their learning over decision making steps.

This paper investigates whether a financial system can be made more stable if financial institutions share risk by exchanging contingent convertible (CoCo) debt obligations. The question is framed in a financial network model of debt and equity interlinkages with the addition of a variant of the CoCo that converts continuously when a bank's equity-debt ratio drops to a trigger level. The main theoretical result is a complete characterization of the clearing problem for the interbank debt and equity at the maturity of the obligations. We then introduce stylized networks to study when introducing contingent convertible bonds improves financial stability, as well as specific networks for which contingent convertible bonds do not provide uniformly improved system performance. To return to the main question, we examine the EU financial network at the time of the 2011 EBA stress test to do comparative statics to study the implications of CoCo debt on financial stability. It is found that by replacing all unsecured interbank debt by standardized CoCo interbank debt securities, systemic risk in the EU will decrease and bank shareholder value will increase.

We prove that if $X$ is a topological space that admits Debreu's classical utility theorem (eg.\ $X$ is separable and connected, second countable, etc.), then order relations on $X$ satisfying milder completeness conditions can be continuously embedded in $\mathbb R^I$ for $I$ some index set. In the particular case where $X$ is a compact metric space, this closes a conjecture of Nishimura \& Ok (2015). We also show that when $\mathbb R^I$ is given a non-standard partial order coinciding with Pareto improvement, the analogous embedding theorem fails to hold in the continuous case.

We establish general versions of a variety of results for quasiconvex, lower-semicontinuous, and law-invariant functionals. Our results extend well-known results from the literature to a large class of spaces of random variables. We sometimes obtain sharper versions, even for the well-studied case of bounded random variables. Our approach builds on two fundamental structural results for law-invariant functionals: the equivalence of law invariance and Schur convexity, i.e., monotonicity with respect to the convex stochastic order, and the fact that a law-invariant functional is fully determined by its behaviour on bounded random variables. We show how to apply these results to provide a unifying perspective on the literature on law-invariant functionals, with special emphasis on quantile-based representations, including Kusuoka representations, dilatation monotonicity, and infimal convolutions.

We discuss when law-invariant convex functionals "collapse to the mean". More precisely, we show that, in a large class of spaces of random variables and under mild semicontinuity assumptions, the expectation functional is, up to an affine transformation, the only law-invariant convex functional that is linear along the direction of a nonconstant random variable with nonzero expectation. This extends results obtained in the literature in a bounded setting and under additional assumptions on the functionals. We illustrate the implications of our general results for pricing rules and risk measures.

Natural and anthropogenic disasters frequently affect both the supply and demand side of an economy. A striking recent example is the Covid-19 pandemic which has created severe industry-specific disruptions to economic output in most countries. Since firms are embedded in production networks, these direct shocks to supply and demand will propagate downstream and upstream. We show that existing input-output models which allow for binding demand and supply constraints yield infeasible solutions when applied to pandemic shocks of three major European countries (Germany, Italy, Spain). We then introduce a mathematical optimization procedure which is able to determine best-case feasible market allocations, giving a lower bound on total shock propagation. We find that even in this best-case scenario network effects substantially amplify the initial shocks. To obtain more realistic model predictions, we study the propagation of shocks bottom-up by imposing different rationing rules on firms if they are not able to satisfy incoming demand. Our results show that overall economic impacts depend strongly on the emergence of input bottlenecks, making the rationing assumption a key variable in predicting adverse economic impacts. We further establish that the magnitude of initial shocks and network density heavily influence model predictions.

This paper presents machine learning techniques and deep reinforcement learningbased algorithms for the efficient resolution of nonlinear partial differential equations and dynamic optimization problems arising in investment decisions and derivative pricing in financial engineering. We survey recent results in the literature, present new developments, notably in the fully nonlinear case, and compare the different schemes illustrated by numerical tests on various financial applications. We conclude by highlighting some future research directions.

We develop a novel procedure for estimating the optimizer of general convex stochastic optimization problems of the form $\min_{x\in\mathcal{X}} \mathbf{E}[F(x,\xi)]$, when the given data is a finite independent sample selected according to $\xi$. The procedure is based on a median-of-means tournament, and is the first procedure that exhibits the optimal statistical performance in heavy tailed situations: we recover the asymptotic rates dictated by the central limit theorem in a non-asymptotic manner once the sample size exceeds some explicitly computable threshold. Additionally, our results apply in the high-dimensional setup, as the threshold sample size exhibits the optimal dependence on the dimension (up to a logarithmic factor). The general setting allows us to recover recent results on multivariate mean estimation and linear regression in heavy-tailed situations and to prove the first sharp, non-asymptotic results for the portfolio optimization problem.

We provide a very brief introduction to typical paths and the corresponding It\^o type integration. Relying on this robust It\^o integration, we prove an existence and uniqueness result for one-dimensional differential equations driven by typical paths with non-Lipschitz continuous coefficients in the spirit of Yamada--Watanabe as well as an approximation result in the spirit of Doss--Sussmann.

In recognition of the transformative opportunities that broadband connectivity presents, the United Nations Broadband Commission has committed the international community to accelerate universal access across the developing world. However, the cost of meeting this objective, and the feasibility of doing so on a commercially viable basis, are not well understood. This paper compares the global cost-effectiveness of different infrastructure strategies for the developing world to achieve universal 4G or 5G mobile broadband. Utilizing remote sensing and geospatial infrastructure simulation, least-cost network designs are developed for eight representative low and middle-income countries (Malawi, Uganda, Kenya, Senegal, Pakistan, Albania, Peru and Mexico), the results from which form the basis for aggregation to the global level. To provide at least 2 Mbps per user, 4G is often the cheapest option, whereas a minimum 10 Mbps per user is cheapest with 5G non-standalone (NSA). The cost of meeting the UN Broadband Commission target of a minimum 10 Mbps per user is estimated at USD 1.4 trillion using 5G NSA, equating to approximately 0.5% of annual GDP for the developing world over the next decade. However, by creating a favorable regulatory environment, governments can bring down these costs by as much as three quarters to USD 0.5 trillion (approximately 0.2% of annual GDP) - and avoid the need for public subsidy. Providing governments make judicious choices, adopting fiscal and regulatory regimes conducive to lowering costs, broadband universal service may be within reach of most developing countries over the next decade.

We revisit the foundational Moment Formula proved by Roger Lee fifteen years ago. We show that when the underlying stock price martingale admits finite log-moments E[|log(S)|^q] for some positive q, the arbitrage-free growth in the left wing of the implied volatility smile is less constrained than Lee's bound. The result is rationalised by a market trading discretely monitored variance swaps wherein the payoff is a function of squared log-returns, and requires no assumption for the underlying martingale to admit any negative moment. In this respect, the result can derived from a model-independent setup. As a byproduct, we relax the moment assumptions on the stock price to provide a new proof of the notorious Gatheral-Fukasawa formula expressing variance swaps in terms of the implied volatility.

We study the impact of weak identification in discrete choice models, and provide insights into the determinants of identification strength in these models. Using these insights, we propose a novel test that can consistently detect weak identification in commonly applied discrete choice models, such as probit, logit, and many of their extensions. Furthermore, we demonstrate that when the null hypothesis of weak identification is rejected, Wald-based inference can be carried out using standard formulas and critical values. A Monte Carlo study compares our proposed testing approach against commonly applied weak identification tests. The results simultaneously demonstrate the good performance of our approach and the fundamental failure of using conventional weak identification tests for linear models in the discrete choice model context. Furthermore, we compare our approach against those commonly applied in the literature in two empirical examples: married women labor force participation, and US food aid and civil conflicts.

Within the context of capital adequacy, we study comonotonicity of risk measures in terms of the primitives of the theory: acceptance sets and eligible, or reference, assets. We show that comonotonicity cannot be characterized by the properties of the acceptance set alone and heavily depends on the choice of the eligible asset. In fact, in many important cases, comonotonicity is only compatible with risk-free eligible assets. The incompatibility with risky eligible assets is systematic whenever the acceptability criterion is based on Value at Risk or any convex distortion risk measure such as Expected Shortfall. These findings qualify and arguably call for a critical appraisal of the meaning and the role of comonotonicity within a capital adequacy context.

Consumer preference elicitation is critical to devise effective policies for the diffusion of electric vehicles in India. For this purpose, we use stated preferences of over 1000 Indian consumers and present the first estimates of the additional purchase price that Indian consumers are willing to pay to improve the electric vehicle attributes (e.g., driving range). We adopt a hybrid choice modelling framework to simultaneously model the willingness to pay and the effect of consumers' latent attitudes (e.g., hedonic and symbolic values) on their likelihood to adopt electric vehicles. We also account for reference dependence by considering a conventional vehicle as the reference alternative and illustrate that the resulting willingness to pay estimates are more realistic. Based on our results, Indian consumers are willing to pay additional USD 10-34 in purchase price to reduce the fast charging time by 1 minute, USD 7-40 to add a kilometre to the driving range of electric vehicle at 200 kilometres, and USD 104-692 to save USD 1 per 100 kilometres in operating cost. These estimates and the effect of attitudes on the likelihood to adopt electric vehicles provide insights about electric vehicle design, marketing strategies, and pro-electric-vehicle policies (e.g., specialised lanes and reserved parking for electric vehicles) to expedite the adoption of electric vehicles in India.