In this paper, we develop the theory of functional generation of portfolios in an equity market of a changing dimension. By introducing dimensional jumps in the market, as well as jumps in stock capitalization between the dimensional jumps, we construct different types of self-financing stock...

The notion of compact city has become an important planning agenda to achieve a sustainable urban future. Although there is no universally accepted definition of a compact city, in terms of land use, the concept generally focuses on high-density and mixed-use development along with the promotion...

We determine the optimal investment strategy in a Black-Scholes financial market to minimize the so-called probability of drawdown, namely, the probability that the value of an investment portfolio reaches some fixed proportion of its maximum value to date. We assume that the portfolio is...

Oft-cited causes of mini-flash crashes include human errors, endogenous feedback loops, the nature of modern liquidity provision, fundamental value shocks, and market fragmentation. We develop a mathematical model which captures aspects of the first three explanations. Empirical features of...

We study a risk sensitive control version of the lifetime ruin probability problem. We consider a sequence of investments problems in Black-Scholes market that includes a risky asset and a riskless asset. We present a differential game that governs the limit behavior. We solve it explicitly and...