In this paper we introduce and solve a class of optimal stopping problems of recursive type. In particular, the stopping payoff depends directly on the value function of the problem itself. In a multi-dimensional Markovian setting we show that the problem is well posed, in the sense that the value is indeed the unique solution to a fixed point problem in a suitable space of continuous functions, and an optimal stopping time exists. We then apply our class of problems to a model for stock trading in two different market venues and we determine the optimal stopping rule in that case.

Democracy often fails to meet its ideals, and these failures may be made worse by electoral institutions. Unwanted outcomes include polarized institutions, unresponsive representatives, and the ability of a faction of voters to gain power at the expense of the majority. Various reforms have been proposed to address these problems, but their effectiveness is difficult to predict against a backdrop of complex interactions. Here we outline a path for systems-level modeling to help understand and optimize repairs to U.S. democracy. Following the tradition of engineering and biology, models of systems include mechanisms with dynamical properties that include nonlinearities and amplification (voting rules), positive feedback mechanisms (single-party control, gerrymandering), negative feedback (checks and balances), integration over time (lifetime judicial appointments), and low dimensionality (polarization). To illustrate a systems-level approach we analyze three emergent phenomena: low dimensionality, elite polarization, and anti-majoritarianism in legislatures. In each case, long-standing rules now contribute to undesirable outcomes as a consequence of changes in the political environment. Theoretical understanding at a general level will also help evaluate whether a proposed reform's benefits will materialize and be lasting, especially as conditions change again. In this way, rigorous modeling may not only shape new lines of research, but aid in the design of effective and lasting reform.

How crypto flows among Bitcoin users is an important question for understanding the structure and dynamics of the cryptoasset at a global scale. We compiled all the blockchain data of Bitcoin from its genesis to the year 2020, identified users from anonymous addresses of wallets, and constructed monthly snapshots of networks by focusing on regular users as big players. We apply the methods of bow-tie structure and Hodge decomposition in order to locate the users in the upstream, downstream, and core of the entire crypto flow. Additionally, we reveal principal components hidden in the flow by using non-negative matrix factorization, which we interpret as a probabilistic model. We show that the model is equivalent to a probabilistic latent semantic analysis in natural language processing, enabling us to estimate the number of such hidden components. Moreover, we find that the bow-tie structure and the principal components are quite stable among those big players. This study can be a solid basis on which one can further investigate the temporal change of crypto flow, entry and exit of big players, and so forth.

A customized internet survey experiment is conducted in Japan to examine how individuals' relative income position influences preferences for income redistribution and individual perceptions regarding income tax burden. I first asked respondents about their perceived income position in their country and their preferences for redistribution and perceived tax burden. In the follow-up survey for the treatment group, I provided information on their true income position and asked the same questions as in the first survey. For the control group, I did not provide their true income position and asked the same questions. I gathered a large sample that comprised observations of the treatment group (4,682) and the control group (2,268). The key findings suggest that after being informed of individuals' real income position, (1) individuals who thought their income position was higher than the true one perceived their tax burden to be larger, (2) individuals' preference for redistribution hardly changes, and (3) irreciprocal individuals perceive their tax burden to be larger and are more likely to prefer redistribution. However, the share of irreciprocal ones is small. This leads Japan to be a non-welfare state.

Widely discredited ideas nevertheless persist. Why do people fail to ``unlearn''? We study one explanation: beliefs are resistant to retractions (the revoking of earlier information). Our experimental design identifies unlearning -- i.e., updating from retractions -- and enables its comparison with learning from equivalent new information. Across different kinds of retractions -- for instance, those consistent or contradictory with the prior, or those occurring when prior beliefs are either extreme or moderate -- subjects do not fully unlearn from retractions and update less from them than from equivalent new information. This phenomenon is not explained by most of the well-studied violations of Bayesian updating, which yield differing predictions in our design. However, it is consistent with difficulties in conditional reasoning, which have been documented in other domains and circumstances.

As job markets worldwide have become more competitive and applicant selection criteria have become more opaque, and different (and sometimes contradictory) information and advice is available for job seekers wishing to progress in their careers, it has never been more difficult to determine which factors in a r\'esum\'e most effectively help career progression. In this work we present a novel, large scale dataset of over half a million r\'esum\'es with preliminary analysis to begin to answer empirically which factors help or hurt people wishing to transition to more senior roles as they progress in their career. We find that previous experience forms the most important factor, outweighing other aspects of human capital, and find which language factors in a r\'esum\'e have significant effects. This lays the groundwork for future inquiry in career trajectories using large scale data analysis and natural language processing techniques.

Embedding value investment in portfolio optimization models has always been a challenge. In this paper, we attempt to incorporate it by first employing principal component analysis (PCA) sector wise to filter out dominant financial ratios from each sector and thereafter, use the portfolio optimization model incorporating second order stochastic dominance (SSD) criteria to derive the final optimal investment. We consider a total of 11 well known financial ratios corresponding to each sector representing four categories of ratios, namely liquidity, solvency, profitability, and valuation. PCA is then applied sector wise over a period of 10 years from April 2004 to March 2014 to extract dominant ratios from each sector in two ways, one from the component solution and other from each category on the basis of their communalities. The two step Sectoral Portfolio Optimization (SPO) model integrating the SSD criteria in constraints is then utilized to build an optimal portfolio. The strategy formed using the former extracted ratios is termed as PCA-SPO(A) and the latter one as PCA-SPO(B).

The results obtained from the proposed strategies are compared with the SPO model and two nominal SSD models, with and without financial ratios for computational study. Empirical performance of proposed strategies is assessed over the period of 6 years from April 2014 to March 2020 using a rolling window scheme with varying out-of-sample time line of 3, 6, 9, 12 and 24 months for S&P BSE 500 market. We observe that the proposed strategy PCA-SPO(B) outperforms all other models in terms of downside deviation, CVaR, VaR, Sortino ratio, Rachev ratio, and STARR ratios over almost all out-of-sample periods. This highlights the importance of value investment where ratios are carefully selected and embedded quantitatively in portfolio selection process.

The problem of portfolio optimization when stochastic factors drive returns and volatilities has been studied in previous works by the authors. In particular, they proposed asymptotic approximations for value functions and optimal strategies in the regime where these factors are running on both slow and fast timescales. However, the rigorous justification of the accuracy of these approximations has been limited to power utilities and a single factor. In this paper, we provide an accuracy analysis for cases with general utility functions and two timescale factors by constructing sub- and super-solutions to the fully nonlinear problem such that their difference is at the desired level of accuracy. This approach will be valuable in various related stochastic control problems.

Time series momentum strategies are widely applied in the quantitative financial industry and its academic research has grown rapidly since the work of Moskowitz, Ooi and Pedersen (2012). However, trading signals are usually obtained via simple observation of past return measurements. In this article we study the benefits of incorporating dynamic econometric models to sequentially learn the time-varying importance of different look-back periods for individual assets. By the use of a dynamic binary classifier model, the investor is able to switch between time-varying or constant relations between past momentum and future returns, dynamically combining different look-back periods and improving trading signals accuracy and portfolio performance. Using data from 56 future contracts we show that a mean-variance investor will be willing to pay a considerable managment fee to switch from the traditional naive time series momentum strategy to the dynamic classifier approach.

The distribution of liquidity within the limit order book is essential for the impact of market orders on the stock price and the emergence of price shocks. Hence it is of great interest to improve the understanding of the time-dependent dynamics of the limit order book. In our analysis we find a broad distribution of limit order lifetimes. Around the quotes we find a densely filled regime with mostly short living limit orders, far away from the quotes we find a sparse filling with mostly long living limit orders. We determine the characteristics of those two regimes and point out the main differences. Based on our research we propose a model for simulating the regime around the quotes.