Nehal Ahmed Shaikh
I'm interested in animanga, artificial intelligence, game theory, math, philosophy, and whatever else fuels the mind. For now, the only interesting information about me publicly available is my CV and GitHub. More shall be shared here soon as ongoing projects unfold (and I learn CSS, HTML, and JavaScript).
Codes
Linear Algebra: an Overview [html][ipynb]
The Cake-eating Problem
Here's an incomplete but interesting problem—a simple finite-horizon dynamic optimization problem.
Suppose that you have a cake of size \(x_0\). At each point of time \(t = 0, 1, \dots, T - 1\), you consume \(c_t\) from the cake, deriving utility \(u(c_t)\) and leaving \(x_{t + 1}\) for the future, i.e, the evolution of the cake is governed by \(x_{t + 1} = x_t - c_t\). We assume that \(u(\cdot)\) is well behaved, differentiable, strictly increasing, and strictly concave; we further assume \(\lim_{c \to 0} u^\prime(c) \to \infty\) and represent your total utility by \[U = \sum_{{t=1}}^{T} \alpha^{t-1}u(c_t)\] where \(\alpha \in [0, 1]\) is the discount factor.
How would you find the optimal path of consumption, \(\{c_t\}_1^T\)?