Research & Projects

Principal Investigator of a sponsored research project investigating Systematic Investment Plan (SIP) strategies across global equity markets through large-scale empirical simulations, statistical inference, and computational finance techniques.

Consider particles with anisotropic surface energy evolve on a substrate towards a shape with minimum surface energy (see Figure 1). We are interested in the evolution of particles and their equilibrium shape (steady state). Further, we want to handle possible topological changes (singularities) without additional efforts. This problem is commonly known as the obstacle problem. We use a level-set approach to solve the obstacle problem: we developed a stable thresholding scheme, which can handle topological changes and approximate anisotropic mean curvature flow, and proved its stability unconditional. Before dealing with the obstacle problem, we surveyed known convolution kernels used in thresholding scheme and we perform their comparison tests to understand the behaviour of error and convergence order, time required for computation, ability to handle sharp corners of particles and evolution of non-convex shapes.

Figure 1: Setup of the mathematical model of a particle evolving on a flat, rigid substrate.

[All figures/content belong to elastoplastic compression program group and Prof. Karel Svadlenka]

The goal is to simulate the evolution of elastoplastic material with energy modelled by E and dissipation given by D. The energy is of neo-Hook type and dissipation distance is slip difference. The setup of the problem is shown in Figure 2. Fundamentally, we desire to solve the minimization problem of sum of E and D at every time step. The problem is solved using FEM and the outcome is compared with lab experiments. My contributions include optimizing and upgrading code, reducing memory usage, and significantly improving computational efficiency. We are exploring the influence of numerical parameters on simulation results and aiming to set parameter ranges based on their roles.

Figure 2: Setup of the elastoplastic deformation problem (boundary conditions).

This research area sits at the intersection of macroeconomics, population economics, and development theory, exploring how long-term economic growth is shaped by choices regarding family size, education, and individual well-being across generations. Using the dynastic Overlapping Generations (OLG) model as its core structural framework—which tracks how different age cohorts interact and pass wealth down families over time—this field analyzes the fundamental balance between fertility choices and investments in human capital. As a country moves through a demographic transition from high birth and death rates to low ones, it triggers a temporary demographic dividend where a booming working-age population can fuel rapid development if effectively utilized. Crucially, modern research expands the definition of human capital beyond traditional schooling to include health; specifically, these generational frameworks now integrate mental health as a critical pillar of productivity, examining how public policies and changing socioeconomic pressures affect parental investment in a child's psychological and emotional development.

This research area explores the boundaries of market efficiency by investigating predictable, time-variant patterns and structural anomalies across global capital markets. Key focuses include analyzing how institutional settlement mechanisms, systematic retail flows, and derivatives execution cycles (such as Futures & Options expirations) interact with market microstructure to create transient liquidity distortions and price pressures on benchmark stock indices. By evaluating these systemic inefficiencies, the field aims to design, backtest, and optimize strategic, rule-based asset accumulation frameworks—such as systematic investment plans—effectively bridging quantitative finance theory with practical portfolio optimization to enhance long-term, risk-adjusted returns.