The Merton problem is the well-known stochastic control problem of choosing consumption over time, as well as an investment mix, to maximize expected constant relative risk aversion (CRRA) utility of consumption. Merton formulated the problem and provided an analytical solution in 1970; since then a number of extensions of the original formulation have been solved. In this note we identify a certainty equivalent problem, i.e., a deterministic optimal control problem with the same optimal value function and optimal policy, for the base Merton problem, as well as a number of extensions. When time is discretized, the certainty equivalent problem becomes a second-order cone program (SOCP), readily formulated and solved using domain specific languages for convex optimization. This makes it a good starting point for model predictive control, a policy that can handle extensions that are either too cumbersome or impossible to handle exactly using standard dynamic programming methods.

The standard rule of soccer penalty shootouts has received serious criticism due to its bias towards the team kicking the first penalty in each round. Therefore, the rule-making body of the sport has decided in 2017 to try alternative designs. This paper offers an extensive overview of eight penalty shootout mechanisms, one of them first introduced here. Their fairness is analysed under three possible mathematical models of psychological pressure. We also discuss the probability of reaching the sudden death stage, as well as the complexity and strategy-proofness of the rules. In the case of stationary scoring probabilities considered here, it remains sufficient to use static rules in order to improve fairness. However, it is worth compensating the second-mover by making it first-mover in the sudden death stage. Our work has the potential to impact decision-makers who can save valuable resources by choosing only theoretically competitive policy options for field experiments.

Neural networks for stock price prediction(NNSPP) have been popular for decades. However, most of its study results remain in the research paper and cannot truly play a role in the securities market. One of the main reasons leading to this situation is that the prediction error(PE) based evaluation results have statistical flaws. Its prediction results cannot represent the most critical financial direction attributes. So it cannot provide investors with convincing, interpretable, and consistent model performance evaluation results for practical applications in the securities market. To illustrate, we have used data selected from 20 stock datasets over six years from the Shanghai and Shenzhen stock market in China, and 20 stock datasets from NASDAQ and NYSE in the USA. We implement six shallow and deep neural networks to predict stock prices and use four prediction error measures for evaluation. The results show that the prediction error value only partially reflects the model accuracy of the stock price prediction, and cannot reflect the change in the direction of the model predicted stock price. This characteristic determines that PE is not suitable as an evaluation indicator of NNSPP. Otherwise, it will bring huge potential risks to investors. Therefore, this paper establishes an experiment platform to confirm that the PE method is not suitable for the NNSPP evaluation, and provides a theoretical basis for the necessity of creating a new NNSPP evaluation method in the future.

In the context of traditional life insurance, the future discretionary benefits ($FDB$), which are a central item for Solvency~II reporting, are generally calculated by computationally expensive Monte Carlo algorithms. We derive analytic formulas for lower and upper bounds for the $FDB$. This yields an estimation interval for the $FDB$, and the average of lower and upper bound is a simple estimator. These formulae are designed for real world applications, and we compare the results to publicly available reporting data.

While patents and standards have been identified as essential driving components of innovation and market growth, the inclusion of a patent in a standard poses many difficulties. These difficulties arise from the contradicting natures of patents and standards, which makes their combination really challenging, but, also, from the opposing business and market strategies of different patent owners involved in the standardisation process. However, a varying set of policies has been adopted to address the issues occurring from the unavoidable inclusion of patents in standards concerning certain industry sectors with a constant high degree of innovation, such as telecommunications. As these policies have not always proven adequate enough, constant efforts are being made to improve and expand them. The intriguing and complicated relationship between patents and standards is finally examined through a review of the use cases of well-known standards of the telecommunications sector which include a growing set of essential patents.

Healthcare workers are more likely to be infected with the 2019 novel coronavirus (COVID-19) because of unavoidable contact with infected people. Although they are equipped to reduce the likelihood of infection, their distress has increased. This study examines how COVID-19 influences healthcare workers' happiness, compared to other workers. We constructed panel data via Internet surveys during the COVID-19 epidemic in Japan, from March to June 2020, by surveying the same respondents at different times. The survey period started before the state of emergency, and ended after deregulation. The key findings are as follows. (1) Overall, the happiness level of healthcare workers is lower than that of other workers. (2) The biggest disparity in happiness level, between healthcare workers and others, was observed after deregulation and not during the state of emergency. After deregulation, the difference was larger by 0.26 points, on an 11-point scale, than in the initial wave before the state of emergency.

I describe a method for estimating agents' perceived returns to investments that relies on cross-sectional data containing binary choices and prices, where prices may be imperfectly known to agents. This method identifies the scale of perceived returns by assuming agent knowledge of an identity that relates profits, revenues, and costs rather than by eliciting or assuming agent beliefs about structural parameters that are estimated by researchers. With this assumption, modest adjustments to standard binary choice estimators enable consistent estimation of perceived returns when using price instruments that are uncorrelated with unobserved determinants of agents' price misperceptions as well as other unobserved determinants of their perceived returns. I demonstrate the method, and the importance of using price variation that is known to agents, in a series of data simulations.

In this paper we explore ways of numerically computing recursive dynamic monetary risk measures and utility functions. Computationally, this problem suffers from the curse of dimensionality and nested simulations are unfeasible if there are more than two time steps. The approach considered in this paper is to use a Least Squares Monte Carlo (LSM) algorithm to tackle this problem, a method which has been primarily considered for valuing American derivatives, or more general stopping time problems, as these also give rise to backward recursions with corresponding challenges in terms of numerical computation. We give some overarching consistency results for the LSM algorithm in a general setting as well as explore numerically its performance for recursive Cost-of-Capital valuation, a special case of a dynamic monetary utility function.

The trustless nature of permissionless blockchains renders overcollateralization a key safety component relied upon by decentralized finance (DeFi) protocols. Nonetheless, factors such as price volatility may undermine this mechanism. In order to protect protocols from suffering losses, undercollateralized positions can be liquidated. In this paper, we present the first in-depth empirical analysis of liquidations on protocols for loanable funds (PLFs). We examine Compound, one of the most widely used PLFs, for a period starting from its conception to September 2020. We analyze participants' behavior and risk-appetite in particular, to elucidate recent developments in the dynamics of the protocol. Furthermore, we assess how this has changed with a modification in Compound's incentive structure and show that variations of only 3% in an asset's dollar price can result in over 10m USD becoming liquidable. To further understand the implications of this, we investigate the efficiency of liquidators. We find that liquidators' efficiency has improved significantly over time, with currently over 70% of liquidable positions being immediately liquidated. Lastly, we provide a discussion on how a false sense of security fostered by a misconception of the stability of non-custodial stablecoins, increases the overall liquidation risk faced by Compound participants.

The financial and economic crisis recently experienced by many European countries has increased demand for timely, coherent and consistent distributional information for the household sector. In the Euro area, most of the NCBs collect such information through income and wealth surveys, which are often used to inform their decisions. These surveys, however, can often suffer from biases, usually caused by non-response and under-reporting behaviours, leading to a mismatch with macroeconomic aggregates. In this paper, we develop a novel allocation method which combines information from a power law (Pareto) model and imputation procedures so to address these issues simultaneously, when only limited external information is available. We provide two important contributions: first, we adjust the weights of observed survey households for non-response bias, then, we correct for measurement error. Finally, we produce distributional indicators for four Euro-Area countries.

Pricing financial derivatives, in particular European-style options at different time-maturities and strikes, is a relevant financial problem. The dynamics describing the price of vanilla options when constant volatilities and interest rates are assumed, is governed by the Black-Scholes model, a linear parabolic partial differential equation with terminal value given by the pay-off of the option contract and no additional boundary conditions. Here, we present a digital quantum algorithm to solve Black-Scholes equation on a quantum computer for a wide range of relevant financial parameters by mapping it to the Schr\"odinger equation. The non-Hermitian nature of the resulting Hamiltonian is solved by embedding the dynamics into an enlarged Hilbert space, which makes use of only one additional ancillary qubit. Moreover, we employ a second ancillary qubit to transform initial condition into periodic boundary conditions, which substantially improves the stability and performance of the protocol. This algorithm shows a feasible approach for pricing financial derivatives on a digital quantum computer based on Hamiltonian simulation, technique which differs from those based on Monte Carlo simulations to solve the stochastic counterpart of the Black Scholes equation. Our algorithm remarkably provides an exponential speedup since the terms in the Hamiltonian can be truncated by a polynomial number of interactions while keeping the error bounded. We report expected accuracy levels comparable to classical numerical algorithms by using 10 qubits and 94 entangling gates on a fault-tolerant quantum computer, and an expected success probability of the post-selection procedure due to the embedding protocol above 60\%.

Like ESG investing, climate change is an important concern for asset managers and owners, and a new challenge for portfolio construction. Until now, investors have mainly measured carbon risk using fundamental approaches, such as with carbon intensity metrics. Nevertheless, it has not been proven that asset prices are directly impacted by these fundamental-based measures. In this paper, we focus on another approach, which consists in measuring the sensitivity of stock prices with respect to a carbon risk factor. In our opinion, carbon betas are market-based measures that are complementary to carbon intensities or fundamental-based measures when managing investment portfolios, because carbon betas may be viewed as an extension or forward-looking measure of the current carbon footprint. In particular, we show how this new metric can be used to build minimum variance strategies and how they impact their portfolio construction.

This study more complex digital platforms in early stages in the two-sided market to produce powerful network effects. In this study, I use Transfer Entropy to look for super users who connect hominids in different networks to achieve higher network effects in the digital platform in the two-sided market, which has recently become more complex. And this study also aims to redefine the decision criteria of product managers by helping them define users with stronger network effects. With the development of technology, the structure of the industry is becoming more difficult to interpret and the complexity of business logic is increasing. This phenomenon is the biggest problem that makes it difficult for start-ups to challenge themselves. I hope this study will help product managers create new digital economic networks, enable them to make prioritized, data-driven decisions, and find users who can be the hub of the network even in small products.