**Core Concept**
A person's false belief in their illness, despite lack of evidence, is a classic example of a psychological phenomenon known as somatic symptom disorder. This condition is characterized by one or more chronic physical symptoms, such as pain or fatigue, that are distressing and result in a significant disruption of daily life.

**Why the Correct Answer is Right**
The correct diagnosis is somatic symptom disorder, which is a type of mental health disorder. This condition is often associated with a high level of anxiety and hypervigilance, leading the individual to focus excessively on their symptoms and seek medical attention repeatedly. The patient's insistence on their illness despite negative investigations is a hallmark feature of this disorder.

**Why Each Wrong Option is Incorrect**
**Option A:** Hypochondriasis is an outdated term that was previously used to describe excessive worry about having a serious illness. However, the term has been replaced by somatic symptom disorder in the DSM-5.
**Option B:** Munchausen syndrome is a factitious disorder where an individual fabricates or exaggerates their symptoms to gain attention and sympathy. While it shares some similarities with somatic symptom disorder, it is a distinct condition.
**Option C:** Factitious disorder is a broader category that includes both Munchausen syndrome (faking symptoms) and Munchausen by proxy (faking symptoms in a child). This option is too broad and does not specifically match the scenario described.
**Option D:** Conversion disorder, also known as functional neurological symptom disorder, is characterized by symptoms that affect motor or sensory function, such as paralysis or numbness. This option does not match the scenario described, which involves a false belief in an illness.

**Clinical Pearl / High-Yield Fact**
Remember the "ABC" of somatic symptom disorder: **A**nxiety, **B**ody-focused preoccupation, and **C**linical significance (i.e., the symptoms cause significant distress or impairment).

**Correct Answer: A. Somatic symptom disorder.**