Deep Learning for Constrained Utility Maximisation

This paper proposes two algorithms for solving stochastic control problems with deep learning, with a focus on the utility maximisation problem. The first algorithm solves Markovian problems via the Hamilton Jacobi Bellman (HJB) equation. We solve this highly nonlinear partial differential equation (PDE) with a second order backward stochastic differential equation (2BSDE) formulation. The convex structure of the problem allows us to describe a dual problem that can either verify the original primal approach or bypass some of the complexity. The second algorithm utilises the full power of the duality method to solve non-Markovian problems, which are often beyond the scope of stochastic control solvers in the existing literature. We solve an adjoint BSDE that satisfies the dual optimality conditions. We apply these algorithms to problems with power, log and non-HARA utilities in the Black-Scholes, the Heston stochastic volatility, and path dependent volatility models. Numerical experiments show highly accurate results with low computational cost, supporting our proposed algorithms.

How Conflicts Affect Land Expansion by Smallholder Farmers: Evidence from Nigeria

The expansion of smallholder farms into larger farm sizes is a key strategy for growing agriculture in sub-Saharan Africa. This strategy could simultaneously expand farm incomes while addressing poverty since the majority of farms in sub-Saharan Africa are smallholder farms. There is limited existing research on the possible role of conflicts in stymying the ability of smallholder farmers to transition into larger-scale farming and on the impacts of conflicts in areas that are not directly within active conflict zones. In this paper, we investigate the impacts of conflict on the ability of smallholder farmers to transition to larger scales in two regions that are not in a traditional conflict zone, by developing a household utility maximisation model to explain choices made by farm households in response to conflict.

Pascal's Mugger Strikes Again

In a well-known paper, Nick Bostrom presents a confrontation between a fictionalised Blaise Pascal and a mysterious mugger. The mugger persuades Pascal to hand over his wallet by exploiting Pascal's commitment to expected utility maximisation. He does so by offering Pascal an astronomically high reward such that, despite Pascal's low credence in the mugger's truthfulness, the expected utility of accepting the mugging is higher than rejecting it. In this article, I present another sort of high value, low credence mugging. This time, the mugger utilises research on existential risk and the long-term potential of humanity to exploit Pascal's expected-utility-maximising descendant. This mugging is more insidious than Bostrom's original as it relies on plausible facts about the long-term future, as well as realistic credences about how our everyday actions could, albeit with infinitesimally low likelihood, affect the future of humanity.

Migration, Remittances, and Entrepreneurship: A Seemingly Unrelated Bivariate Probit Approach

The aim of this paper is to examine the interdependence between the decision to invest in entrepreneurship and the receipt of remittances. Firstly, a conceptual framework is developed within the household utility-maximisation model, wherein households are seen to make decisions on entrepreneurship and remittances simultaneously. Guided by this, the model is specified and estimated, employing the seemingly unrelated bivariate probit model upon a random sample stemming from the Kosovo population census. The findings suggest broad support for the household approach. As expected, the two decisions are simultaneously determined and, while remittances have a positive impact on entrepreneurship, no evidence is found for the statistical importance of migration. Household entrepreneurial behaviour is determined by demographic characteristics, income, relative wealth, education, and type of area.