Find valid range of q for outcome probabilities

Q: Find valid range of q for outcome probabilities

This question evaluates understanding of probability distributions and the formulation of arbitrage conditions using linear algebra, testing competencies in probability theory, inequality constraints, and financial modeling within the Software Engineering Fundamentals / Data Science domain.

Q: How do I approach Software Engineering Fundamentals interview questions?

Software Engineering Fundamentals questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master software engineering fundamentals interviews.

Question

Loading...

You have a 3-outcome experiment with mutually exclusive outcomes:

Outcome 1 occurs with probability $q$
Outcome 2 occurs with probability $q^2$
Outcome 3 occurs with probability $1 - q - q^2$

Find the full range of $q$ for which these form a valid probability distribution.
Suppose there are three tradable “tickets” (assets) and you are allowed to take long/short positions. Each ticket has a known payoff in each of the 3 outcomes. Let:

$x \in \mathbb{R}^3$ be the portfolio positions (positive = long, negative = short)
$p \in \mathbb{R}^3$ be today’s prices of the tickets
$A \in \mathbb{R}^{3\times 3}$ be the payoff matrix where $A_{ij}$ is the payoff of ticket $j$ in outcome $i$

Write the “construct an arbitrage portfolio” condition as a matrix/vector inequality system (i.e., a feasibility problem using $A$ , $p$ , and $x$ ).

Find valid range of q for outcome probabilities

Solution

Comments (0)

Find valid range of q for outcome probabilities

Overview

Solution

Comments (0)