Decisions in Economics and Finance最新文献

Amortization plans are well-known financial operations to repay interest-bearing loans through a sequence of periodic payments. Since amortization plans are generally settled according to the compound interest law, some questions arise about the supposed presence of anatocism and the consequent legal matters. In this paper, we derive the traditional amortization plans by means of an alternative approach, based on the concept of fair amortization and without assuming a financial law. We find that the traditional amortization plan with constant installments can be derived in this way and the supposed presence of anatocism is excluded. An investigation on the possible anatocism, in case of delayed payment of interest, completes the discussion.

Shannon entropy is the most common metric for assessing the degree of randomness of time series in many fields, ranging from physics and finance to medicine and biology. Real-world systems are typically non-stationary, leading to entropy values fluctuating over time. This paper proposes a hypothesis testing procedure to test the null hypothesis of constant Shannon entropy in time series data. The alternative hypothesis is a significant variation in entropy between successive periods. To this end, we derive an unbiased sample entropy variance, accurate up to the order (O(n^{-4})) with n the sample size. To characterize the variance of the sample entropy, we first provide explicit formulas for the central moments of both binomial and multinomial distributions describing the distribution of the sample entropy. Second, we identify the optimal rolling window length to estimate time-varying Shannon entropy. We optimize this choice using a novel self-consistent criterion based on counting significant entropy variations over time. We corroborate our findings using the novel methodology to assess time-varying regimes of entropy for stock price dynamics by presenting a comparative analysis between meme and IT stocks in 2020 and 2021. We show that low entropy values correspond to periods when profitable trading strategies can be devised starting from the symbolic dynamics used for entropy computation, namely periods of market inefficiency.

This paper deals with the positivity condition of an infinite-dimensional evolutionary equation, associated with a control problem for the optimal consumption over space. We consider a spatial growth model for capital, with production generating endogenous growth and technology of the form AK. We show that for certain initial data, even in the case of heterogeneous spatial distribution of technology and population, the solution to an auxiliary control problem that is commonly used as a candidate for the original problem is not admissible. In particular, we show that initial conditions that are non-negative, under the auxiliary optimal consumption strategy, may lead to negative capital allocations over time.

Abstract

We consider a class of non-cooperative N-player nonzero-sum stochastic differential games with singular controls, in which each player can affect a linear stochastic differential equation in order to minimize a cost functional which is quadratic in the state and linear in the control. We call these games linear-quadratic-singular stochastic differential games. Under natural assumptions, we show the existence of open-loop Nash equilibria, which are characterized through a linear system of forward-backward stochastic differential equations. The proof is based on an approximation via a sequence of games in which players are restricted to play Lipschitz continuous strategies. We then discuss an application of these results to a model of capacity expansion in oligopoly markets.

We present a geometric approach to portfolio theory with a focus on risk-adjusted returns, in particular Jensen’s alpha. We find that while the alpha/beta approach has severe limitations, especially in higher dimensions, only minor conceptual modifications (e.g., using orthogonal Sharpe ratios rather than risk-adjusted returns) are needed to identify the efficient trading strategies. We further show that, in a complete market, the so-called market price of risk vector is identical to the growth optimal Kelly vector, albeit expressed in coordinates of a different basis. This implies that a derivative, having an orthogonal Sharpe ratio of zero, has a price given by the minimal martingale measure.

We propose a minimal set of commonly acceptable principles to consistently formulate amortization schedules in accordance with different contractual clauses. Our goal is bringing to the fore premises that are sometimes left implicit, and yet seem to draw a wide consensus in practice. We demonstrate by means of examples how these principles may be used to deal with risk or financial innovations, and to fill gaps arising from unforeseen contingencies.

With increasing numbers of Australians in or entering retirement, the modelling of functional disability and health status is critical to the insuring and financing of retirement risks for both governments and individuals. The multi-state modelling of these risks underlies projections of the population by functional disability status, the estimation of healthy life expectancy, the sustainable financing of public aged care and innovations in private long-term care insurance. Developing a model for the Australian population is challenging because of the lack of longitudinal health and mortality data for older Australians. We use the cross-sectional data in the Survey of Disability, Ageing and Carers for years 1998, 2003, 2009, 2012, 2015 and 2018, providing prevalence of functional disability and illness across 20 years, to estimate a multi-state transitions model that best explain the observed changes of prevalence in Australia. We develop and estimate for the first time an Australian model for transitions between five states (healthy, disabled but not ill, ill but not disabled, disabled and ill, and dead) using age, sex and trend factors for those aged 60 or greater. Functional disability is defined by autonomy of activities of daily living. Illness is defined by chronic illness conditions including heart problems, diabetes, lung disease, and stroke. Model estimation is done numerically. Using the fitted model, we estimate yearly transition probabilities, life expectancy of retirees and projected population distributions by functional disability and health states. We also provide a comparison of the results with previous studies.

The distribution of productivity levels, and its evolution over time, is a research topic of utmost importance in empirical and theoretical economics. On the theory side, simple analytical models, involving intertemporal optimization, typically characterize agents’ investment decisions about ways to upgrade technology and enhance productivity. The prototypical model endogenously splits the productivity distribution in two: the right-hand side of the distribution is populated by innovators; the left-hand side is occupied by agents who follow a strategy of adoption or imitation. Given the assumptions of the model, the productivity of innovators grows at a constant rate (which directly depends on a constant probability of innovation). The evolution of the productivity of adopters may, in turn, implicate complex dynamics. Because the pace of productivity growth for adopters depends on the shape of the productivity distribution, different distributions might induce distinct growth paths, some of them potentially leading to the emergence of nonlinearities, such as limit cycles and chaos. This study investigates the presence of nonlinearities in technology adoption, for different configurations of the productivity distribution. Under reasonable parameterizations, endogenous fluctuations emerge as a plausible long-term equilibrium.

We investigate the ability of the Lee–Carter model to effectively estimate the gender gap ratio (GGR), the ratio between the male death rates over the female ones, by using a Cox–Ingersoll–Ross (CIR) process to provide a stochastic representation of the fitting errors. The novelty consists in the fact that we use the parameters characterizing the CIR process itself (long-term mean and volatility), in their intrinsic meanings, as quantitative measures of the long-term fitting attitude of the Lee–Carter model and synthetic indicators of the overall risk of this model. The analysis encompasses 25 European countries, to provide evidence-based indications about the goodness of fit of the Lee–Carter model in describing the GGR evolution. We highlight some stylized facts, namely systematic evidence about the fitting bias and the risk of the model across ages and countries. Furthermore, we perform a functional cluster analysis, allowing to capture similarities in the fitting performance of the Lee–Carter model among countries.