This thesis is composed of two parts. The first part is based on a paper co-authored with Fabio Trojani, entitled ”A Unifying Convex Analysis Framework for Penalized Least Squares”. In this paper, we establish a framework for studying the statistical properties of Penalized Least Squares Estimators (PLSEs)with con- vex penalties, which is applicable both under a regular and a singular design. Our approach borrows from a reinterpretation of PLSEs as proximity operators and Moreau's decomposition of these operators. This allows for a general characterization of the asymp- totic properties of PLSEs, which only depends on suit- able functional transformations of the PLSE limit penalty. Exploiting our approach, we propose convenient Oracle PLSEs for singular designs exhibiting the grouping effect, and valid bootstrap approximations for the associated asymptotic distributions. The second part consists in a paper co-authored with Sofonias Kor- saye and Fabio Trojani, entitled ”Smart Stochastic Discount Factors”, which proposes a novel no-arbitrage framework exploiting convex asset pricing constraints to study investors' marginal utility of wealth or, more generally, Stochastic Discount Factors (SDFs). We establish a duality between minimum dispersion SDFs and penalized portfolio selection problems, building the foundation for characteriz- ing the feasible trade- offs between a SDF's pricing accuracy and its comovement with systematic risks. Empirically, a minimum variance CAPM–SDF produces a Pareto optimal tradeoff. This SDF only depends on two distinct risk fac- tors: A traded mar- ket factor and a minimum variance excess return that bounds the mispricing of risks unspanned by market shocks.