We consider closed-form approximations for European put option prices within the Heston and GARCH diffusion stochastic volatility models with time-dependent parameters. Our methodology involves writing the put option price as an expectation of a Black-Scholes formula and performing a second-order Taylor expansion around the mean of its argument. The difficulties then faced are simplifying a number of expectations induced by the Taylor expansion. Under the assumption of piecewise-constant parameters, we derive closed-form pricing formulas and devise a fast calibration scheme. Furthermore, we perform a numerical error and sensitivity analysis to investigate the quality of our approximation and show that the errors are well within the acceptable range for application purposes. Lastly, we derive bounds on the remainder term generated by the Taylor expansion.

We consider an investor, whose portfolio consists of a single risky asset and a risk free asset, who wants to maximize his expected utility of the portfolio subject to the Value at Risk assuming a heavy tail distribution of the stock prices return. We use Markov Decision Process and dynamic programming principle to get the optimal strategies and the value function which maximize the expected utility for parametric as well as non parametric distributions. Due to lack of explicit solution in the non parametric case, we use numerical integration for optimization

We consider explicit approximations for European put option prices within the Stochastic Verhulst model with time-dependent parameters, where the volatility process follows the dynamics $dV_t = \kappa_t (\theta_t - V_t) V_t dt + \lambda_t V_t dB_t$. Our methodology involves writing the put option price as an expectation of a Black-Scholes formula, reparameterising the volatility process and then performing a number of expansions. The difficulties faced are computing a number of expectations induced by the expansion procedure explicitly. We do this by appealing to techniques from Malliavin calculus. Moreover, we deduce that our methodology extends to models with more general drift and diffusion coefficients for the volatility process. We obtain the explicit representation of the form of the error generated by the expansion procedure, and we provide sufficient ingredients in order to obtain a meaningful bound. Under the assumption of piecewise-constant parameters, our approximation formulas become closed-form, and moreover we are able to establish a fast calibration scheme. Furthermore, we perform a numerical sensitivity analysis to investigate the quality of our approximation formula in the Stochastic Verhulst model, and show that the errors are well within the acceptable range for application purposes.

Technological cumulativeness is considered one of the main mechanisms for technological progress, yet its exact meaning and dynamics often remain unclear. To develop a better understanding of this mechanism we approach a technology as a body of knowledge consisting of interlinked inventions. Technological cumulativeness can then be understood as the extent to which inventions build on other inventions within that same body of knowledge. The cumulativeness of a technology is therefore characterized by the structure of its knowledge base, which is different from, but closely related to, the size of its knowledge base. We analytically derive equations describing the relation between the cumulativeness and the size of the knowledge base. In addition, we empirically test our ideas for a number of selected technologies, using patent data. Our results suggest that cumulativeness increases proportionally with the size of the knowledge base, at a rate which varies considerably across technologies. At the same time we find that across technologies, this rate is inversely related to the rate of invention over time. This suggests that the cumulativeness increases relatively slow in rapidly growing technologies. In sum, the presented approach allows for an in-depth, systematic analysis of cumulativeness variations across technologies and the knowledge dynamics underlying technology development.

Given a stock price process, we analyse the potential of arbitrage by insiders in a context of short-selling prohibitions. We introduce the notion of minimal supermartingale measure, and we analyse its properties in connection to the minimal martingale measure. In particular, we establish conditions when both fail to exist. These correspond to the case when the insider's information set includes some non null events that are perceived as having null probabilities by the uninformed market investors. These results may have different applications, such as in problems related to the local risk-minimisation for insiders whenever strategies are implemented without short selling.

We consider portfolio optimization under a preference model in a single-period, complete market. This preference model includes Yaari's dual theory of choice and quantile maximization as special cases. We characterize when the optimal solution exists and derive the optimal solution in closed form when it exists. The payoff of the optimal portfolio is a digital option: it yields an in-the-money payoff when the market is good and zero payoff otherwise. When the initial wealth increases, the set of good market scenarios remains unchanged while the payoff in these scenarios increases. Finally, we extend our portfolio optimization problem by imposing a dependence structure with a given benchmark payoff and derive similar results.

We consider an investor, whose portfolio consists of a single risky asset and a risk free asset, who wants to maximize his expected utility of the portfolio subject to managing the Value at Risk (VaR) assuming a heavy tailed distribution of the stock prices return. We use a stochastic maximum principle to formulate the dynamic optimisation problem. The equations which we obtain does not have any explicit analytical solution, so we look for accurate approximations to estimate the value function and optimal strategy. As our calibration strategy is non-parametric in nature, no prior knowledge on the form of the distribution function is needed. We also provide detailed empirical illustration using real life data. Our results show close concordance with financial intuition.We expect that our results will add to the arsenal of the high frequency traders.

Approximately half of the global population does not have access to the internet, even though digital access can reduce poverty by revolutionizing economic development opportunities. Due to a lack of data, Mobile Network Operators (MNOs), governments and other digital ecosystem actors struggle to effectively determine if telecommunication investments are viable, especially in greenfield areas where demand is unknown. This leads to a lack of investment in network infrastructure, resulting in a phenomenon commonly referred to as the 'digital divide'. In this paper we present a method that uses publicly available satellite imagery to predict telecoms demand metrics, including cell phone adoption and spending on mobile services, and apply the method to Malawi and Ethiopia. A predictive machine learning approach can capture up to 40% of data variance, compared to existing approaches which only explain up to 20% of the data variance. The method is a starting point for developing more sophisticated predictive models of telecom infrastructure demand using publicly available satellite imagery and image recognition techniques. The evidence produced can help to better inform investment and policy decisions which aim to reduce the digital divide.

In behavioural economics, a decision maker's preferences are expressed by choice functions. Preference robust optimization (PRO) is concerned with problems where the decision maker's preferences are ambiguous, and the optimal decision is based on a robust choice function with respect to a preference ambiguity set. In this paper, we propose a PRO model to support choice functions that are: (i) monotonic (prefer more to less), (ii) quasi-concave (prefer diversification), and (iii) multi-attribute (have multiple objectives/criteria). As our main result, we show that the robust choice function can be constructed efficiently by solving a sequence of linear programming problems. Then, the robust choice function can be optimized efficiently by solving a sequence of convex optimization problems. Our numerical experiments for the portfolio optimization and capital allocation problems show that our method is practical and scalable.

The paper presents the professor-student network of Nobel laureates in economics. 74 of the 79 Nobelists belong to one family tree. The remaining 5 belong to 3 separate trees. There are 350 men in the graph, and 4 women. Karl Knies is the central-most professor, followed by Wassily Leontief. No classical and few neo-classical economists have left notable descendants. Harvard is the central-most university, followed by Chicago and Berlin. Most candidates for the Nobel prize belong to the main family tree, but new trees may arise for the students of Terence Gorman and Denis Sargan.

Aiming to describe the wealth distribution evolution, several models consider an ensemble of interacting economic agents that exchange wealth in binary fashion. Intriguingly, models that consider an unbiased market, that gives to each agent the same chances to win in the game, are always out of equilibrium until the perfect inequality of the final state is attained. Here we present a rigorous analytical demonstration that any system driven by unbiased binary exchanges are doomed to drive the system to perfect inequality and zero mobility.

We introduce mlOSP, a computational template for Machine Learning for Optimal Stopping Problems. The template is implemented in the R statistical environment and publicly available via a GitHub repository. mlOSP presents a unified numerical implementation of Regression Monte Carlo (RMC) approaches to optimal stopping, providing a state-of-the-art, open-source, reproducible and transparent platform. Highlighting its modular nature, we present multiple novel variants of RMC algorithms, especially in terms of constructing simulation designs for training the regressors, as well as in terms of machine learning regression modules. At the same time, mlOSP nests most of the existing RMC schemes, allowing for a consistent and verifiable benchmarking of extant algorithms. The article contains extensive R code snippets and figures, and serves the dual role of presenting new RMC features and as a vignette to the underlying software package.